FORCE, MASS AND ACCELERATION
3 marks · NormalA sports car and a large van each experience the same unbalanced force when accelerating from rest. The mass of the van is four times larger than the mass of the car.
Use the relationship F = m × a to explain, in detail, which vehicle will have greater acceleration and why.
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The sports car will have greater acceleration because acceleration is inversely proportional to mass when the force is the same. Since the van's mass is four times the car's, its acceleration will be a quarter that of the car.
Also accept: The car will accelerate more quickly because for the same force, a lower mass produces a higher acceleration. The van’s acceleration is four times less than the car’s.; Acceleration is a = F/m, so when mass increases, acceleration decreases if the force is constant. Therefore, the car, with smaller mass, has greater acceleration.
Common mistakes: Just stating the car is faster without linking to equation; Mixing up the proportionality
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Marking points
B1 · 1 mark · Identifies that acceleration is greater for the car
B2 · 1 mark · Links explanation to the equation F = m × a (or a = F/m)
B3 · 1 mark · Explains correctly that when the mass is four times larger, acceleration is four times smaller if force is unchanged
Worked solution
The sports car will have greater acceleration, because:
• F = m × a, so a = F/m.
• Both vehicles experience the same force, but the van's mass is four times greater.
• This means the van's acceleration is one quarter that of the car's, so the car accelerates faster.