MOMENTUM
5 marks · HardA 1500 kg car is moving at 12 m/s along a straight road. The driver presses the brakes and brings the car to a complete stop in 2.8 s.
Calculate the change in momentum of the car.
Calculate the average braking force exerted on the car.
Explain in physics terms why increasing the stopping time would affect the force experienced by the car.
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.
Show answer
(a) -18000 kg m/s · must show p = m × v, change in p = p_final - p_initial
(b) -6430 N · must show force = change in momentum / time
(c) A longer stopping time means the force is smaller for the same change in momentum because F = Δp / t. · must show F = Δp / t, force decreases as time increases
Common mistakes: Forgetting to use change in momentum (not just final or initial momentum); Substituting values incorrectly
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Correctly substitutes to find initial and final momentum and calculate their difference.
A1 (a) · 1 mark · Correct final answer: -18000 kg m/s.
M2 (b) · 1 mark · Applies force = change in momentum / time with correct values. (follow-through)
A2 (b) · 1 mark · Correct numerical answer and negative sign: -6430 N (accept rounding to nearest 10 N). (follow-through)
B1 (c) · 1 mark · States or uses F = Δp / t to explain that increasing time decreases the force for the same Δp.
Worked solution
(a) Initial momentum:
Final momentum: 0 (car stops)
(b) Average force:
(c) Increasing the stopping time reduces the average force for the same change in momentum because
so increasing t results in a smaller F.