Learning objectives
- Distinguish distance from displacement.
- Calculate speed and acceleration.
- Interpret simple distance-time and velocity-time graphs.
- Use correct SI units.
Distance and displacement
Distance is the total length of the actual path travelled. It is a scalar quantity. Displacement is the shortest straight-line change from initial position to final position and includes direction.
Distance is always non-negative. Displacement can be zero even when distance is not zero, such as after completing one full lap and returning to the starting point.
Speed, velocity and acceleration
Average speed equals total distance divided by total time. Average velocity equals displacement divided by total time. Velocity includes direction.
Acceleration is the rate of change of velocity. Positive acceleration can increase speed, while negative acceleration in the direction of motion is often called deceleration.
Reading graphs
The slope of a distance-time graph represents speed. A steeper slope indicates greater speed. A horizontal line means the object is at rest.
The slope of a velocity-time graph represents acceleration. The area under a velocity-time graph represents displacement.
Practice questions with explanations
Try each question before opening the answer. The explanation shows the reasoning, not only the final response.
Q1. A runner completes one 400 m lap and stops at the start. What are distance and displacement?
Answer: Distance is 400 m; displacement is 0 m.
Explanation: The runner travelled 400 m but finished at the original position.
Q2. Calculate average speed for 150 m travelled in 30 s.
Answer: 5 m/s.
Explanation: Speed = distance ÷ time = 150 ÷ 30.
Q3. What is the SI unit of speed?
Answer: Metre per second (m/s).
Explanation: Distance is measured in metres and time in seconds.
Q4. How does velocity differ from speed?
Answer: Velocity includes direction.
Explanation: Speed is scalar, while velocity is vector.
Q5. A car’s velocity changes from 10 m/s to 20 m/s in 5 s. Find acceleration.
Answer: 2 m/s².
Explanation: Acceleration = (20 − 10) ÷ 5.
Q6. What does a horizontal distance-time graph show?
Answer: The object is at rest.
Explanation: Distance does not change as time passes.
Q7. What does the slope of a distance-time graph represent?
Answer: Speed.
Explanation: Slope is change in distance divided by change in time.
Q8. What does the slope of a velocity-time graph represent?
Answer: Acceleration.
Explanation: Slope is change in velocity divided by time.
Q9. Can an object have constant speed but changing velocity?
Answer: Yes.
Explanation: In circular motion the direction changes, so velocity changes.
Q10. What does the area under a velocity-time graph give?
Answer: Displacement.
Explanation: Velocity multiplied by time gives displacement.