The quantities of motion

Every motion measurement is a physical quantity with a number and a unit. CCEA uses these SI units:

• Distance (and displacement) — measured in metres (m).
• Speed (and velocity) — measured in metres per second (m/s).
• Rate of change of speed (acceleration) — measured in metres per second squared (m/s²).
• Time — measured in seconds (s).

Everyday speeds: a person walks at roughly 1.5 m/s, a sprinter runs at around 10 m/s, and a car on a town road travels near 13 m/s (about 30 mph). Knowing these helps you sense-check an answer.

Match the unit

Speed = distance ÷ time

Speed tells you how quickly an object covers distance. CCEA wants you to recall and use the average speed equation:

There is a second form CCEA lists for steady changes of speed — the average of the start and end speeds:

Your turn — average speed

Scalars vs vectors

A scalar has size only. A vector has size and direction. CCEA pairs them up:

• Distance is a scalar; displacement is a vector — both in metres (m).
• Speed is a scalar; velocity is a vector — both in m/s.
• Rate of change of speed is a scalar; acceleration is a vector — both in m/s².

Watch out: distance and displacement are only equal when the motion is in a perfectly straight line. Walk a full lap of a track and your distance is 400 m, but your displacement is zero — you finished where you started.

Scalar or vector?

Tap a quantity, then tap the box it belongs in.

Velocity is rate of change of displacement

Where speed only says "how fast", velocity says "how fast and in which direction". CCEA defines it through displacement:

For a steady change of velocity in one direction, you can also use the average of the start and end velocities:

Watch out: two cars can have the same speed (30 m/s) but different velocities if they travel in different directions. Velocity is a vector — change the direction and you change the velocity, even if the speed stays the same.

Your turn — average velocity

Acceleration = change in velocity ÷ time

Acceleration is how quickly velocity changes. For motion in one direction:

Watch out: acceleration is the change in velocity, not the velocity itself. An object can be moving fast yet have zero acceleration (steady velocity). A negative acceleration — slowing down — is called retardation in CCEA.

Your turn — acceleration

Distance–time graphs: slope = speed

On a distance–time graph the gradient (slope) is the speed. The steeper the line, the faster the object. A flat line means it is stationary.

Reading a distance–time graph

Velocity–time graphs: slope & area

A velocity–time graph packs in two pieces of information CCEA expects you to extract:

• the slope (gradient) is the acceleration;
• the area under the line is the distance moved (displacement).

Watch out: don't confuse the two graphs. On a distance–time graph the slope is the speed; on a velocity–time graph the slope is the acceleration and the area underneath is the distance.

Your turn — gradient of a v–t graph

Your turn — area under a v–t graph

Your turn — rearranging speed

Which graph tells you what?

Tap a feature on the left, then its meaning on the right.

The relationships to know

You've covered the whole of CCEA Unit 1.1 — Motion: quantities and units, speed and average speed, scalars and vectors, displacement, velocity and acceleration, and motion graphs. Press Finish to see your score.