Speed and velocity
Speed is the distance travelled per unit time; it is a scalar. Velocity is speed in a stated direction; it is a vector. Average speed uses total distance over total time, while instantaneous speed is the speed at one instant.
Key idea
speed = distance ÷ time, so v = s ÷ t (unit m/s). acceleration a = (v − u) ÷ t, where u is initial and v is final velocity (unit m/s²).
Acceleration
Acceleration is the rate of change of velocity. A body speeds up when acceleration acts in the direction of motion, and slows down (decelerates) when it acts against the motion, giving a negative value. Steady speed in a straight line means zero acceleration.
Worked example
A car starts from rest (u = 0) and reaches 20 m/s in 8.0 s. a = (v − u) ÷ t = (20 − 0) ÷ 8.0 = 2.5 m/s².
Motion graphs
On a distance–time graph, the gradient equals speed: a steeper line means faster motion, and a horizontal line means the body is at rest. On a speed–time graph, the gradient equals acceleration and the area under the line equals the distance travelled.
Remember
- Speed is scalar; velocity is a vector.
- Acceleration is measured in m/s².
- Area under a speed–time graph = distance travelled.