Motion: speed, velocity and acceleration

Scalars vs vectors

• Scalar quantities have size only: distance, speed, mass.
• Vector quantities have size AND direction: displacement, velocity, acceleration, force.

Distance is the total path length travelled. Displacement is the straight-line distance from start to finish in a stated direction.

Speed and velocity

speed = distance / time. Units: m/s.

velocity = displacement / time. Same units, but with a direction (e.g. 20 m/s east).

Acceleration

acceleration = change in velocity / time taken.

a = (v - u) / t

Units: m/s^2. Negative acceleration is deceleration.

SUVAT for uniform acceleration (Higher tier)

For motion with constant acceleration, WJEC uses:

v^2 = u^2 + 2 a s

Where:

• u = initial velocity (m/s)
• v = final velocity (m/s)
• a = acceleration (m/s^2)
• s = displacement (m)

Worked example: a car accelerates from rest at 2 m/s^2 over 50 m. Find v.

• u = 0, a = 2, s = 50.
• v^2 = 0 + 2 x 2 x 50 = 200.
• v = sqrt(200) = 14.1 m/s.

Distance-time and velocity-time graphs

• Distance-time: gradient = speed. Horizontal line = stationary.
• Velocity-time: gradient = acceleration. Area under the line = distance travelled.

WJEC exam tip

Watch for trick questions that ask for displacement when an object returns to start. The distance can be 100 m but the displacement zero. Read every motion question for the precise quantity asked.