Speed and motion

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Speed, distance and time

The speed of an object using the following equation

speed (m/s)= distance (m)time (s)

The units of speed depend upon what distance and time are measured in and must be consistent. For example when speed has the

units of m/s, the distance used must be in metres and the time in seconds.

To show working, values must be substituted into the equation and either rearranged or converted to a ‘maths triangle’.

Average speed considers the total distance travelled and total time, whereas instantaneous speed only considers the distance travelled over a short period of time (in that ‘instant’).

Distance - time graphs

The distance an object travels can be plotted against time.

A horizontal line means the object is stationary (e.g. time 20-40 s).

A straight line means a constant speed (times 0-20 and 40-60 s).

The gradient of the line gives the object’s speed.

A steeper line means a greater speed.

The change in distance and time can be read from the graph so the speed can be calculated.

For example the speed from 40 to 60 seconds = 30 / 20 = 1.5 m/s

The average speed = total distance / total time = 40 / 60 = 0.67 m/s

Acceleration

Acceleration is the rate with which an object’s speed is changing.

Acceleration (m/s2)= change in speed (m/s)time (s)

If a car’s speed increases from 10 to 30 m/s in 5 seconds, its acceleration = (30 - 10) / 5 = 20 / 5 = 4 m/s2

Note the units of acceleration are m/s2.

Terminal velocity

Terminal velocity is reached when a falling object is at its maximum speed. Considering a parachute jumper performing a skydive:

Initially they accelerate due to weight being the only force.

As they accelerate, the frictional force (air resistance) opposing their motion gets bigger and the acceleration decreases to zero.

They are then moving at a constant speed known as terminal velocity.

Opening their parachute will cause frictional forces (air resistance) to increase and become larger than their weight, so they decelerate (slow down).

As they slow down, air resistance decrease until it balances their weight again and they travel at a new, lower terminal velocity.