Physics

1.1 - Speed, Velocity & Displacement

6 min

Calculating speed and velocity

Typical speedsOutside your course

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Calculating speed from distance and time

For an object moving at a constant speed (or velocity):

Distance (or displacement) = speed (or velocity) × time

$Speed (or velocity) = \frac{distance (or displacement)}{time}$

Average speed over a whole journey

When speed varies across a journey:

$Average speed = \frac{total distance travelled}{total time taken}$

To measure the speed of an object moving at constant speed: time how long it takes to travel a measured distance, then divide the distance by the time.

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Worked example - Speed and time of a cat

A cat walks 25 m along a straight path in 50 s. Find its speed, then how long it would take to walk 100 m at that same speed.

The same grey cat drawn at each end of a blue arrow labelled 25 m, with a stopwatch reading 50 s beside the cat on the right.

Step 1 - Find the speed

$Speed = \frac{distance}{time} = \frac{25}{50} = 0.5 m/s$

Step 2 - Rearrange for time

$Time = \frac{distance}{speed}$

Step 3 - Find the time to walk 100 m

$Time = \frac{100}{0.5} = 200 s$

So the cat walks at 0.5 m/s and takes 200 s to cover 100 m.

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Average speed and rate of change of speed

When an object speeds up or slows down steadily, its average speed is:

$Average speed = \frac{initial speed + final speed}{2}$

This works only while the speed changes at a steady rate.
The rate of change of speed measures how quickly speed changes:

$Rate of change of speed = \frac{final speed - initial speed}{time taken}$

It's measured in m/s², the same unit as acceleration. Rate of change of speed has no direction, while acceleration (the rate of change of velocity) does.

end of notes

Key points to remember

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1.2 - Scalar & Vector QuantitiesNext up