Linear and Non-linear Motion

Linear and Non-linear Motion

Every time you move from home to school or any other place, you always see other bodies such as vehicles, animals and many others in motion relative to you. Have you ever noticed the path followed during motion? For example, how is the motion of a train (Figure. 1.1 (a) different from that of a ceiling fan in Figure. 1.1 (b)?

In this chapter, you will be able to attempt activities to measure distance an short time intervals, and also use data to calculate the speed and acceleration of a moving object and explain their implications.

1.1: Linear Motion

1.1.1: Distance and Displacement
When a body moves from one place or point to another, how do you know how far it has travelled? What happens to its position as it moves? How would you tell or know where the body is heading if its direction is not specified?

Activity 1.1
Investigating the difference between distance and displacement
Key question: What is the difference between distance and displacement?
What you need: Note book,relevant textbook
Initial question: What is distance?

What to do (In groups):

1. Study Figure 1.2 to answer the questions 2 to 6 below.
2. Make research to know more about distance and displacement.

Conclusion and Application
3.Suppose your move from home to a friend’s home to pick him up to go
to school;
(a) What distance will you cover?
(b) How far will you be from home?
4.If your mother wants to go to school, tell her the distance and direction of the school from home.
5. If after classes you return home from school following the same path;
(a) What will be your total distance?
(b) Determine your displacement.
6.Discuss the difference between distance and displacement.

Example 1.1

1. A boy moved on straight road from Point P to R through S as shown in
   Figure 1.3. Calculate;
   (a) distance covered
   (b) displacement

1.During supervision of exams, a teacher moved 6 m east, from corner A of the class, then 2 m south, 6 m west and finally 2 m north back to A as shown in
Figure 1.4. Determine the distance he covered and his displacement.
2. Mary moved from class to the dormitory via the dinning hall as shown in Figure 1.5. Determine the distance she covered and her displacement.
3.An athlete runs along a semicircular path of radius 10 m from A to B as shown in Figure 1.4. Calculate

(a) the distance he covered.
(b) his displacement.
1.12: Speed and Velocity
Whenever a body is in motion, it is important to know how fast or slow it is moving. How is it possible to determine this?
Activity 1.2 Determining the speed of a body Key question: How is speed measured?
What you need: Bicycle, 6 learners, tape measure, a field and 3 stop clocks,

Initial question: What is speed?
What to do (In groups)

1. Mark two points at extreme ends of the field and note the distance.
2. Chose three members from the group (one will walk, the second one will run, and the third one will ride the bicycle).
3. Let them stand on the same starting line.
4. Start off the learner and the stop clocks simultaneously.
   Conclusion and Application
   5.Who reached the other end first?
   6.What time did each of them take?
   7.Determine them speed and velocity of each (include the S.l unit of speed).
   8.Who of the three moved fastest?
   9.How is speed and time related?
   10.From your results, when is a body said to be moving slowly or fast?
5. Discuss why it is important to know the speed of moving objects?

Note:
Speed of body is the rate of change of distance of a body with time. Speed is given by;

Knowing the speed at which the body travels alone cannot describe its motion clearly without direction. This brings in the aspect of velocity. Thus, velocity is the rate of change of distance moving in a particular direction or rate of change of displacement of a body.
Displacement

1. An athlete runs a 100 m south in 2 minutes . Determine his or her velocity.
2. A security guard moves along the perimeter wall of a bank as shown in
   Figure 1.7. Determine his speed and velocity, for each of the sides of the wall.

3. The graph in Figure 1.8 shows motion of a boda boda cycle. What is his speed between points A and B?

1.1.3: Average Speed and Velocity
When you board a taxi to move from Kampala to Jinja and along the way the taxi encounters traffic lights ,traffic jam, busy trading centres and many others,What do you think happens to the speed of the taxi during the journey? How would you estimate its average speed for the whole journey?

Activity 1.3 Determining the average speed of a body Key question: Why is average speed of a body determined?
What you need: Classroom or hall, stop clock and a tape measure. Initial question: What is average speed?
What to do (In groups):

1. Measure the distance between the corners of the class or hall
2. Let one person move around classroom once while;
   a) walking
   b) running
   Use the stop clock to measure the time he/she uses in each case.
   Conclusion and Application)
   3.What was the speed of the person when he was;
   a) walking
   b) running
   4.Determine his/her average speed.
   5.Suppose you move from Kampala to Mbale in a bus. How is the speed of the bus along the journey?
   6.What determines your response in part (5)
   7.Why is average speed of a body determined?

Self Check!

1. A car moves along a straight road ABC as shown in the Figure 1.9maintains an average speed of 90 km/h between points A and B and36 km/h between points B and C.

Calculate the:
(a) Total time taken in seconds by the car between points A and C
(b) Average speed in meters second of the car between gnints A and C

2. The graphs in Figure 1.10 and 1.11 represent motion of a cyclist and a vehicle respectively.

(a) How is speed obtained from a distance-time graph?
(b) Comment on the speed from the two graphs.
(c) Calculate the speed of the cyclist.
(d) Determine the average speed of the vehicle.

1.1.4: Acceleration
There are many cases where a moving body needs to increase or decrease its speed along the journey depending on the situation. For instance, assuming you are riding a bicycle on a steep slope what would you do if you are moving up the hill or sloping down the hill?

Activity 1.4 Understanding acceleration
Key question: Explain the difference between acceleration and deceleration.
What you need: Note book, pen, internet resource, relevant textbook
Initial question : What is meant by the term ” acceleration”
What to do (in groups):

1. Use the ICT or relevant textbook and research about acceleration and deceleration.
2. Study the pictures shown in Figure 1.12 and answer the questions which follow.

3.What should the boy in Figure 1.12. (a) do if he is to reach school in time?
4.The vehicle in Figure 1.12 (b) realises that there is a pothole ahead. Give
some of the expected actions of the driver/car.
5.Basing on your answers in step (3) and (4), how are the changes in motion affecting the bodies involved?
6.Giving reasons, in which of the case, in step (3) or (4) is the body accelerating or decelerating?
Note: A body accelerates if its velocity increases uniformly in a given time.
Therefore acceleration is given by;

When the velocity of the body decreases in a particular interval of time, then the body is decelerating. In this case the final velocity is less than the initial velocity, therefore deceleration is a negative acceleration.

Self Check!

1. Ataxi in Figure 1.13 (a) starts from rest and attains a velocity of 20 ms-l in 3 seconds. Determine its acceleration.
2. The velocity of a buffalo in Figure 1.13 (b) changed from 5 ms-1 to 25 ms-l in 8 seconds after being chased by a lion. Calculate the buffalo’s acceleration.

3.
A boy riding a bicycle at 15ms•l realises that he is about to knock a pedestrian and reduces the velocity to 4 ms-l in 5 seconds. Determine whether the boy is accelerating or decelerating?
Measuring Acceleration of a Body
Acceleration of a body can be measured using a ticker timer which prints dots on a long paper tape attached on a moving body at regular intervals as shown in Figure 1.14. You will learn to measure acceleration of a body in activity 1.5.

Activity 1.5 Measuring acceleration of a body
Key question: How is acceleration of a body determined using a ticker tape timer?
What you need: Power source, ticker timer, ticker tape, runway, trolley,
wooden block, ICT resource, relevant text book.
Initial question: When is a body said to move with uniform velocity?
What to do (In groups):

1. Plan and carry out an investigation on how to measure acceleration of a body using a ticker timer,using the given materials.
   Conclusion and Application
   2What is frequency?
   3.Explain using a dot diagram the motion depicted by a ticker-tape timer for;
   (a) a fast-moving object
   (b) a slow moving object
   (c) an object moving with a constant velocity
   (d) an object accelerating.
   4.Make a short report for the motion of the trolley, for your investigation carried out in (1)
   5.Suggest other uses of a ticker-timer.

Note:
The closer the dots are on the tape, the slower the object moved. The further apart the dots are on the tape, the faster the object moved. A ticker-timer consists of an electric vibrator which vib ates at a frequency of 50 Hz, and thus make 50 dots per second. Hence the time taken to make one dot,
(time period) is 1/50 second, or 0.02s.

Example 1.1
The ticker-tape in Figure 1.15 was produced by a trolley moving down a tilted runway. If the ticker-tape timer produced 50 dots per second, find the acceleration of the trolley.

2. A trolley pulls a paper tape through a ticker timer which has a frequency of 40 Hz. If the distance between two consecutive dots is 4 cm, find the speed of the trolley
3. in: (a) cms-l (b) ms I
4. The ticker timer printed dots on a ticker tape as shown in Figure 1.17.
   Assuming it vibrates at frequency of 20 Hz, calculate;
   a) Initial velocity b) Final velocity c) Acceleration

A paper tape dragged through a ticker timer by a trolley has the first ten dots covering a distance of 4 cm and the next ten dots covering a distance of 7 cm. If the frequency of the ticker timer is 50 Hz.

(a)In which direction is the tape pulled?
(B)Find the initial speed of the trolley.
(C)What is the speed of the trolley at B?
(D)What is the acceleration of the trolley between A and B?

1.1.5: Free-fall
Very many times we see objects falling or rising through the air, For instance, what happens to you when you jump? What does it mean for an object to fall freely? What happens to the speed of the bodies as they fall?
Activity 1.6 Investigating free fall
Key question: How do objects behave during free fall motion?
What you need: Stone (size of your fist), piece of chalk, book, a shoe,a paper Initial question: When is a body said to fall freely?
What to do (In groups):

1. Hold a stone and a piece of chalk at a height above your head.
2. Release them at the same time.
3. Repeat steps (1) and (2) with other objects.
   Conclusion and Application)
4. Which force acts on the objects as they fall through space?

5.Did the objects reach the ground at the same time? Explain your observation.
6.Describe the motion of the objects as they fall freely.
7.Explain whether objects decelerate or accelerate as they fall.
8.Suggest the name given to the acceleration of freely falling objects
9.Discuss any other cases where free-fall motion occurs.

1.1.6: Graphical Representation of Linear Motion
The motion of a body can be best understood by drawing a motion-time graph. These graphs show how basic physical quantities like displacement, velocity or acceleration relate with time.

Activity 1.7 | Drawing and Interpreting velocity-time graphs
Key question: Analyse how objects behave during linear motion.
What you need: Graph book, pencil,lCT resource and relavant text book.
Initial question: What is linear motion?
What to do (In groups):

1. Using the ICT or a relevant textbook, research about;
   (a) distance-time,
   (b) velocity-time graphs for linear motion.
2. Analyse the graphs in Figure 1.18 and answer the questions in your
   notebook.

I Conclusion and Application

3. Draw distance-time and velocity-time graphs for
   (a) A stationary object.
   (b) An object moving with;
   i) uniform velocity
   ii) uniform acceleration

iii) non-uniform velocity
iv) unifoim retardation
v) free-fall motion

4. Interpret the graphs in Figure 1.18 and describe the motion of the car, truck and a boda-boda.

Self Check!
I. Using graphs, describe the motion of the ball moving on a surface shown in Figure 1.19 (a) and (b).

2. A lift carrying people starts from the third floor and stops on the sixth floor of a building after 20s. Sketch a velocity-time graph for the motion of the lift. Show how you would use your sketch to determine the distance between the third and sixth floor of the building.
3. Table 1.1 shows the results obtained in an experiment to describe the motion of a car. Plot a displacement-time graph to represent the motion. Determine the average velocity of the car.

Table 1.2 shows the relationship between Velocity of a bicycle and time. Plot a velocity-time graph to represent the motion. Find the total distance covered by the bicycle. Table 1.2

1.1.8: Equations of Motion
The physical quantities which describe the motion of a body in a straight line are related using three equations. You will learn more about them in activity 1.8.

Key question: How is distance determined using the equations of motion
What you need: ICT, relevant physics text book.
Initial question: From the definition of acceleration state the equation relating v,u,t and a
What to do (In groups):

1. Write down the 3 equation of linear motion.
2. Give the meaning of each of the symbols or terms used in the equations in (i)
   I Conclusion and Application
   DR. NABBANJA ACCELERATES UNIFORMLY AT 4Ms-2 FROM HER CAR PARKING FOR 20 SECONDS ON HER WAY TO THE HOSPITAL
3. Determine her final velocity after the 20 seconds.
4. Use the second equation of linear motion to determine, the distance she covers in this time.
5. From the third equation, find the distance she covers in this time.
6. Compare your results from 4 and 5
   1

1.A body starts from rest and moves with uniform acceleration of 2 ms-2 in a
straight line.
(a) What is its velocity after 5 s?
(b) How far has it travelled after this time?
(c) After how long will the body be 100 m from its starting point?
2.The velocity of a car is retarded from 10 ms-l to 4 ms-1 in 2 s. What is the D

deceleration of the car?
3.A train has a speed of 60 km/h and its speed 5 s later is 70 km/h. (a) Calculate its acceleration in ms-2.
(b) Whatwill after other 2s ifthe acceleration remains the same?
(c) How long will it take to reach 105 km/h at this acceleration?
4.A body starts from rest and reaches a speed of 5 ms•l after travelling with uniform acceleration in a straight line for 2 s.
(a) Calculate the acceleration of the body.
(a) Find the distance travelled during that time.
5.A body starts from rest and accelerates uniformly to a velocity of 10 ms•l in 2 s. It maintains this velocity for 4 s before accelerating uniformly again for another
5s. The body then retards to rest in 2 s.
(a) Calculate the acceleration of the body.

1.2: Newton’s Laws of Motion
In the earlier sections you learnt how to describe motion of a body using graphs, numbers and statements. In this section we ‘Shall predict the motion further using laws of motion which were investigated by sir Isaac Newton. These laws describe the relationship between force and motion of a body.

1.2.1: Newton’s First law of Motion
Suppose you place a book on the table, what will happen to its position after sometime? Why do you think brakes are applied in all moving objects like bicycles, motor bikes, vehicles among others? How does this relate to the speed of the bodies?
Activity 1.9
Investigating Newton’s first law of motion
Key question: How is the behaviour of bodies at rest or uniform motion?
What you need: trolley or toy car, small wooden block, stopper, and a runway
(about 1.5 m), ball, and a table.
Initial uestion: What is mean

What to do (in groups):

1. Place a book on the table and leave it there for 2 minutes.
2. Set up the run way and fix a stopper at the lowest end as shown i Figure 1.20.
   3• Hold the trolley at the highest point of the runway and place a wooden block on top of it.

4. Release the trolley and observe its motion.
   Conclusion and Application
5. In which state of motion is the book?
6. Explain why,the book is in the state (5)
7. Explain what happens to the wooden block once the trolley hits the stopper.
8. In which state of motion is the wooden block before and after hitting the stopper?
9. Under what conditions will the state of motion of the block change.
10. State Newton’s first law of motion.
11. Compare your observations made in part (1) and part (4) with NeMon’s first
    law of motion.
12. Suggest situations in everyday life to which Newton’s first law Of motion applies.
13. Using the ICT or relevant physics textbook, research about Newton’s ISt law of motion.

Newton’s 1st law of motion is also called the law of inertia. Inertia is the reluctance of a body to move, when at rest or to stop when in motion.

Self Check!

1. Explain why it is advisable to fasten seat belts whenever you board any automobile.
2. State and explain what happens to the passengers in an over-speeding vehicle when brakes are suddenly applied

1.3: Linear Momentum
Momentum is one of the common words used especially in sports. For instance what does it mean for a team to have momentum? In addition, why do you think a long jumper as shown in Figure 1.22 will
need to first run as fast as possible if she is to reach the furthest mark? In this section you will learn more about momentum in Physics.

Activity 1.10 Investigating linear momentum Key question: Explain the meaning of momentum.
What you need: Hammers (light and heavy hammer), 2 wooden blocks, 4 identical pieces of nails.
Initial question: What is velocity?
Caution! Take care not to hit your fingers with the hammer.
What to do (In groups):

Figure. 1.22 (a) hitting the nail with a small hammer, (b) hitting the nail with a big hammer

1. Using a small hammer carefully drive the;
   (a) first nail gently into the piece of wood
   (b)the second one very hard as shown in Figure 1.23 (a).
2. Repeat step (1) with a big hammer as in Figure 1.23 (b).
   Conclusion and Application
3. Compare the depth to which the two nails enter the piece of wood for both.
4. How will the force at which any of the hammers hits the nail affects the
   depth of penetration.
5. Which of the two hammers drives the nail into the piece of wood deeper
   regardless of the force used to hit it? Give a reason.
6. Explain the meaning of linear momentum.
   Self Check!
7. Determine the momentum of a cheetah of mass 45 kg chasing an antelope
   at 10 m/s.
8. A car of mass 1500 kg covered a distance of 100 m in 2.5 seconds. Find its momentum.

3. A racing car of mass 1200 kg increased its velocity from 10 ms-l to 30 ms-l in 2 seconds. Find the change in momentum of the car.
   1.2.2: Newton’s Second Law of Motion
   If you are to kick a ball and want it to accelerate faster, what do you consider?
   In which direction will its acceleration be?

Investigating Newton’s second law of motion
Activity 1.11
Key question: What is the relationship between rate of change momentum
and the applied force?
What you need: ICT resource, a relevant textbook, 2 office chairs which
rollers, two learners (one small, the other fat)
Initial question: What is meant by momentum?
What to do (in groups):

1. Let the learners sit on the two chairs respectively.
2. Push the two learners around class.
   Conclusion and Application
   3.Compare the force required to set the two learners in motion.
   4.How will the size of force affect the velocity of the learners?
   5.When the learners are in motion, which one of them can be stopped easily? Explain why?
   6.Make a suitable conclusion about the relationship between the force, mass and acceleration of a body.
   7.Suggest applications of Newton’s second law of motion in everyday life.

Self Check!
If the mass of a sliding block is tripled and at the same time the net force on it is tripled, How does the resulting acceleration compare with the original acceleration?

2. Calculate the acceleration if you push with a 20 N horizontal force against a 2 kg
   block on a horizontal friction- free table.
3. Figure 1.21 shows a man pushing a car of mass 2,000 kg with a force of 50 N. What will
   be the car’s acceleration?

4. A car has a mass of 1000 kg. What is the acceleration produced by a force of 2000 N?
5. How much force, or thrust, must a 30,000 kg jet plane develop to achieve an acceleration of 1.5 ms-2?

1.2.3: Newton’s Third Law of Motion
Activity 1.12 Understanding the Newton’s third law of motion
Key question: Explain the third law of motion.
What you need: Rubber band, bag ,Physics textbook, ICT resources.
Initial question: What are balanced forces?
What to do (In groups):
1.Let one person carry the bag either on his head or by the hands.
2.Using the hands, stretch the rubber band gently and then hardly. Note what is observed as you pull the rubber band.
3.Let another person in the group move around class as you observe the
contact between the shoe sole and the ground.
4.Use the internet or textbook and research about Newton’s third law of motion.

Conclusion and Application
5. Compare the forces between the;

(b)rubber band and the fingers.
(b) bag and the hand
(c) Shoe sole and the ground
Comment about the size and the direction of the forces.
Basing on your observations, draw a suitable conclusion about the forces between any two bodies in contact.
State Newton’s third law of motion.
Suggest other situations in everyday life where Newton’s third law of
motion applies.
1.3.2 Collisions and Impulse
We always experience collisions such as the ones shown in Figure 1.24 in our everyday lives, what do you think happens when bodies collide? What is the impact of such collisions?

Collisions are classified into elastic and inelastic collisions. In activity 1.13, you
will learn more about these types.
Exploring collisions and Impulse
Activity 1.13
Key question: the of energy and momentum in cnllisions.
What you need: ICT resource and relavant text book.
Initial question: What is a collision?
What to do (In groups):

1. Conduct a research about the following;
   (a) Conservation of linear momentum.
   (b) elastic collision
   (c) Inelastic collision
   (d) impulse.
2. Carry out an investigation to demonstrate how linear momentum is conserved in collisions.
   ‘Conclusion and Apphcavon
   3.Mention the types of collisions.
   4.Suggest the differences between the types of collisions.
   Explain the effect of a force during impact when it acts for a;
   (a) short time.
   (b) long time.
   6.What is the relationship between impulse and change in momentum of bodies after collision.
   7.Discuss conservation of both kinetic energy and momentum in the two collisions.

Note: When two or more bodies collide, momentum is conserved. The law of conservation of linear momentum states that, provided no external force acts on a system of colliding bodies, the total momentum before collision is equal to the total momentum after collision. Consider two bodies A and B with masses MA and MB moving with velocities UA and UB respectively. Suppose the two bodies collide and move with velocities VA and VB respectively. The law of conservation of linear momentum follows that; Total Initial momentum = Total final momentum mALIA + MBLIB = mAVA +

Self Check!

1. A particle of mass 200 g moving at 30 ms-l hits a stationary particle of mass 100 g so that they stick and move together after impact. Calculate the velocity with which they move after collision,
2. A body of mass 2 kg travelling at 8 ms•l, collides with a body of mass 3 kg travelling at 5 ms•l in the same direction. If after collision the two bodies move together. Calculate the velocity with which the
   two bodies move.
3. A body of mass 20 kg travelling at 5 ms•l collides with another stationary body of mass of 10 kg and they move separately in the same direction if the velocity of the 20 kg mass after collision was 3 ms-l, calculate the velocity with which 10 kg mass will move.
4. A military tanker of mass 4 tonnes moving at 12 ms-l collides head on with another of mass 3 tonnes moving at 20 ms-l. After collision, they stick together and move as one body. Ignoring the effect of friction, find their common velocity.
5. What breaking force is needed to bring a car weighing 1,500 kg and moving at 30 rns•l to stop 20 s after the brake is applied?
6. A student kicks a stone of mass 0.5 kg and accelerates it from rest to 10 ms-l. The impact lasts 0.01 s. He then decides to kick a football of the same mass to give it the same speed. The impact lasts 0.1 s. Which kick is likely to hurt him less? Explain your answer.

1.4: Motion in a Viscous Fluid
You probably know that it is easier to move in air than in a pool of water. Why is this so? In addition, why does water flow easily compared to honey? In this section you will explore more about motion in viscous fluids.

1.4.1: Terminal Velocity
Suppose you drop a stone through a fluid say air, what do you think happens to its speed as it falls? Is there a point when the body’s speed does not change any more? What happens to the body in such a state? In activity 1.14, you Will find out how falling objects attain terminal velocity.
Activity 1.14 Determing terminal velocity of a body Key question: Describe the motion of bodies through a viscous fluid. What you need: glass jar (1 m long), cooking oil, 4 steel ball bearings of known
diameters, stop clock(s), a metre rule, rubber bands, magnet (to remove the ball bearings from oil),lCT resource, relevant text book. Initial question: What do you
nderstand by constant velocity?

5. Repeat step (4) for other ball Figure. 1.25 ball bearing falling through oi
   bearings.
   Conclusion and Application
   What is viscosity and terminal velocity?
   6.Compare the time intervals for all the ball bearings.
   7.Explain your observation in (7) above.
   8.Measure the length AB and hence determine the terminal velocity Of the.
   ball bearings.
6. State the forces that act on the ball bearing as it falls through the oil.
7. When does a body attain terminal velocity?

12. Discuss factors which affect terminal velocity of a body.
13. State at least three (3) applications of terminal velocity.
    Bodies falling through fluids accelerate until they reach a certain velocity when the resultant force on them is zero. In this state, the body falls with a uniform velocity called terminal velocity.

1.figure 1.26 shows the graph of velocity against time for a small steel ball alling in a viscous liquid.
(a) Describe the motion of the steel ball as represented by regions;
(i) OA
(ii) BC

(b) Explain why the velocity between B and C is constant.

2. Explain how parachutes help a sky diver to land safely on the ground
   1.4.1: Air Resistance
   All objects moving through air experience air resistance. You have probably felt this resistance especially when you move on bicycles or motorcycles. How can air resistance be minimised?

1.4.1: Air Resistance
All Objects moving through air experience air resistance. You have probably felt this resistance especially when you move on bicycles or motorcycles. How can air resistance be minimised?

the effect of air resistance on bodies
Key question: Explain how air resistance affects bodies in motion.
What you need: Two plain papers, ICT resource, relevant text book.
Initial question: What is air resistance?
What to do (in groups):

1. Fold one of the papers and leave the other one flat.
2. Hold the papers at the same height above the ground.
3. Release the papers and observe their motion.
   Conclusion and Application
4. Identify the forces that act on the papers as they fall.
5. Compare the motion of the two papers.
6. Explain why one of the papers reaches the ground very fast and the other takes longer.

7. Basing on your answers, analyse Figure 1.27 (a) and (b) and explain why the bodies can move through air efficiently.

1.5: Non-linear Motion
In the previous sections, you have learnt about motion of bodies in a straight line. In this section we shall focus on motion in curved paths.
1.5.1: Uniform Circular Motion
You must have observed objects moving along a circular path for example a stone whirled on a string or a car negotiating a corner. What do you thin keeps these bodies in such a path?
Activity 1.16 Demonstrating motion in a circle
Key question: Describe the motion of a body taking a circular path.
What you need: piece of chalk, and a string, ICT resource , relevant text book.

Initial question: What do you understand by a circular path?
What to do (In groups):
I. Tie a piece of chalk on a string.

2. Make the piece of chalk move in a circular path.
3. Sketch the graph of the motion of the piece of chalk.
   Conclusion and A plication
   4.Explain the force that keeps the piece of chalk in a circular path. What is its direction?
   5.Suppose the thread breaks, which path will the chalk take? Explain Why?
   6.Determine the speed of the piece of chalk in one complete revolution.
   7.Comment about the direction and magnitude of;
   a) velocity
   b) acceleration of the piece of chalk.
   8.Suggest examples of circular motion in everyday life.

1.6: Vector and Scalar Quantities
Physical quantities are grouped into vector and scalar, depending on their size and direction. Find out more about these quantities in activity 1.17.
Activity 1.17 Understanding vector and scalar quantities
Key question: With example, distinguish between scalar and vector
What you need: Five learners, rope, desk, ICT resource relevant text book.
Initial question: What is the difference between size and direction?
Part (a)

What to do (In groups):
1.Let the four learners move through 2m from a common point of origin.
2.Make an observation about their movement.
3.Once they are back at the common point let the learner move through 2m to the right
4.Make an observation about their movement.
5.Now let the learner move through 3m from the common point of origin.
6.Once they are back, let them move through 3m to the North from the common point of origin
Conclusion and Application*

7. How different are the observations in (2),(4) and (6) above?
8. What is the difference between scalar quantities and vector quantities?
9. Give example of scalar and vector quantities

Part (b)
What you need: rope, learners, table, desk
What to do (In groups):

1. Let two members of your group push the desk as you observe, to the same side.
2. Now, let three other people stand on the opposite of the desk and push the desk at the same time with the other two.
3. Use the rope and other learners to demonstrate;
   (a) opposite forces on the rope.
   (b) perpendicular forces on a body.
   Conclusion and Application
4. Using illustrations, explain how the resultant force is determined in steps (1) to (3).
5. Why is it important to determine resultant forces on a body?
6. Explain the effect of a resultant force on the acceleration of the body.

Chapter 1 Summary
In this chapter you have learnt that:
Linear motion is the motion of bodies in straight line.
Physical quantities which describe linear motion, these include; distance,
displacement, speed, velocity, average speed and average velocity acceleration and deceleration.
Representation of motion of bodies on graphs and interpreting the motion.
The three equations of motion which relate the quantities of motion,
The three NeMon’s laws of motion which describe the relationship between force and motion of the body.
Linear momentum and the law of conservation of linear momentum in collisions.
The types of collisions which include; elastic and inelastic collisions.
Motion in a viscous fluid: which includes terms like terminal velocity and air resistance
Vector and scalar quantities and how to determine the resultant force of a number of forces.
Non-linear motion which includes uniform circular path.