Motion

Vectors and Scalars

Vector quantities have both size and direction. Examples of vector quantities are velocity, displacement, acceleration and force.

Scalar quantities have size but no direction. Examples of scalar quantities are speed, distance and mass.

Distance and Displacement

When total distance travelled by and object is calculated, we take no account of the direction in which it travels. Distance is scalar.

Displacement is defined as the distance moved in a particular direction. It id a vector quantity. The diagram represents a man walking on a football field. He starts at P and walks 50m due east - a displacement of 50m. He then walks 50m due north. 

His total distance travelled would be the distance from P to Q to R. However, his displacement would be the direct distance between his starting point and ending point, i.e, the direct distance between P and R.

Speed

Speed is defined as the rate of change of distance or distance moved per second. It is a scalar quantity. If speed does not vary (if it is constant or uniform) then

Distance is measured in metres per second 

Velocity

Velocity is defined as the rate of change of displacement or displacement per second. It is a vector quantity. If velocity is constant then

The unit of velocity is metre per second

For velocity to be constant, both the speed and direction must be constant.

Acceleration

Acceleration is defined as the rate of change of velocity i.e. the change of velocity per second. If acceleration is constant then

The unit of acceleration is metres per second squared

Acceleration is a vector quantity.

Representation motion using graphs

We use graphs to represent and analyse motion. The most useful to us are graphs of displacement against time, and velocity against time.

Constant Velocity

Ia a car is moving at a constant velocity of 

then every second it will travel a distance of 15 metres in the same direction.

Two graphs can represent this motion:

Displacement/time graph

The graph below represents the car's motion., The gradient of the line is 60/4 = 15. The gradient of a displacement/time graph always represents the velocity.

Velocity/time graph

The gradient of the graph represents the acceleration. In the example below the velocity constant, so the gradient and acceleration are zero.

The area under a velocity/time graph represents the distance travelled. So in 4 seconds, are = 15 x 4 = 60 and the distance travelled is 60m.

Velocity/time graphs are more useful than distance/time graphs. All four quantities are represented on a velocity/time graph: velocity, time, distance and acceleration.

Uniform Acceleration

If a car starts from rest and has an acceleration of 5ms^-2 each second its velocity increases by 5ms^-1

We can represent this in a velocity/time graph as shown below.

We can use the graph to calculate the distance travelled in 6 seconds. Remember that the distance travelled is represented by the are under the graph. The triangle has an area of

The distance travelled in 6 seconds is 90m.