MOTION IN A STRAIGHT LINE

In mechanics, we are interested in trying to understand the motion of objects. In this chapter, the motion of objects in 1 dimension will be discussed.

Speed and Velocity

Speed and Velocity

Speed is how fast something moves.

Velocity is speed with a direction.

Saying Ariel the Dog runs at 9 km/h (kilometers per hour) is a speed.

But saying he runs 9 km/h Westwards is a velocity.

Imagine something moving back and forth very fast: it has a high speed, but a low (or zero) velocity.

Speed

Speed is measured as distance moved over time.

Speed = DistanceTime

We can also use these symbols:

Speed = ΔsΔt

Where Δ (“Delta“) means “change in”, and

• s means distance (“s” for “space”)
• t means time

Units

Speed is commonly measured in:

• meters per second (m/s or m s^-1), or
• kilometers per hour (km/h or km h^-1)

A km is 1000 m, and there are 3600 seconds in an hour, so we can convert like this (see Unit Conversion Method to learn more):

1 m1 s × 1 km1000 m × 3600 s1 h = 3600 m · km · s1000 s · m · h = 3.6 km1 h

So 1 m/s is equal to 3.6 km/h

Average vs Instantaneous Speed

The examples so far calculate average speed: how far something travels over a period of time.

But speed can change as time goes by. A car can go faster and slower, maybe even stop at lights.

So there is also instantaneous speed: the speed at an instant in time. We can try to measure it by using a very short span of time (the shorter the better).

Constant Speed

When the speed does not change it is constant.

For constant speed, the average and instantaneous speeds are the same.

Velocity

Velocity is speed with a direction.

It is actually a vector …

… as it has magnitude and direction

Because the direction is important velocity uses displacement instead of distance:

Speed = DistanceTime

Velocity = DisplacementTime in a direction.