The difference between speed and velocity
4 marks · HardA cyclist travels in a straight line and accelerates from an initial velocity of to a final velocity of in 3.0 seconds. Calculate the cyclist’s acceleration. Explain what the negative and positive signs of velocity indicate, and describe what happens to the cyclist’s motion over this time.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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2.0\,\mathrm{m/s}^2 m/s^2 (±0.05)
Also accept: 2; 2.00
Common mistakes: Taking the magnitude only and ignoring the sign; not using negative sign for initial velocity; mixing up initial and final velocities.
Show mark scheme and worked solution
Marking points
M1 · 1 mark · Clearly substitutes initial and final velocity (with signs) and time into the formula .
A1 · 1 mark · Correct evaluation of . (follow-through)
A2 · 1 mark · Correct final answer with correct unit (). (follow-through)
B1 · 1 mark · Clear explanation of what the negative/positive sign of velocity means, and the change in direction (e.g., cyclist changes direction of motion).
Worked solution
Step 1: Write the formula for acceleration.
Given: initial velocity , final velocity , time .
Step 2: Interpretation — The negative sign for initial velocity means the cyclist was moving in one direction; the positive sign for final velocity means the cyclist is now moving in the opposite direction. The change from negative to positive shows the cyclist decelerated (reduced speed to zero), stopped momentarily, then accelerated in the opposite direction.