Mechanics
Speed, Velocity and Acceleration
Learning Objectives
What you should be able to do after this lesson.
- Define speed, velocity, and acceleration, and state their SI units
- Distinguish between scalar quantities (speed) and vector quantities (velocity)
- Calculate average speed, velocity, and acceleration using standard equations
- Interpret the gradient of distance-time and velocity-time graphs
Lesson Notes
Key definitions, diagrams, and relationships to remember.
Speed and Velocity
Speed is the distance travelled per unit time. It is a scalar quantity — it has magnitude only, with no direction. Velocity is the rate of change of displacement. It is a vector quantity — it has both magnitude and direction. Two objects can have the same speed but different velocities if they are moving in different directions.
average speed = distance travelled ÷ time taken (unit: m/s)
velocity = displacement ÷ time taken (unit: m/s, in a stated direction)
Acceleration
Acceleration is the rate of change of velocity. An object accelerates whenever its speed changes, its direction changes, or both — so acceleration, like velocity, is a vector quantity.
acceleration = change in velocity ÷ time taken = (v − u) ÷ t (unit: m/s²)
where u = initial velocity, v = final velocity, t = time taken
Distance-Time and Velocity-Time Graphs
On a distance-time graph, the gradient represents speed: a steeper line means a faster speed, and a flat horizontal line means the object is stationary. On a velocity-time graph, the gradient represents acceleration, and the area under the graph represents the distance travelled.
Worked Example
Follow each step before attempting the practice worksheet.
A car accelerates uniformly from rest to 20 m/s in 8 seconds. Calculate its acceleration.
Using acceleration = (v − u) ÷ t:
u = 0 m/s (starts from rest)
v = 20 m/s
t = 8 s
acceleration = (20 − 0) ÷ 8 = 2.5 m/s²
The car accelerates at 2.5 m/s².
End-of-lesson quiz
Quick check before you mark the lesson complete.
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