To stop a 960-kg car traveling at 25 m/s in a time of 15 s requires an average force of magnitude

Question

BlackTom AI · Accepted Answer

We start by identifying the given quantities: mass m = 960 kg, initial speed u = 25 m/s, final speed v = 0 m/s, and stopping time Δt = 15 s.

First, compute the change in momentum (impulse) needed to stop the car: Δp = m(v − u) = 960(0 − 25) = −24,000 kg·m/s. The magnitude of the impulse is 24,000 kg·m/s.

Next, relate impulse to average force: F_avg = Δp / Δt. Substituting the numbers gives F_avg = 24,000 / 15 = 1,600 N. The sign is negative if we talk about deceleration, but the question asks for the magnitude, so we report 1,600 N.

Now evaluate each answer option:
- 3200 N: This would require a change in momentum of 3200 N × 15 s = 48,000 kg·m/s, which is twice the actual impulse, so this is too large.
- 4800 N: This would correspond to 4800 × 15 = 72,000 kg·m/s, again far larger than the needed impulse, making this incorrect.
- 1600 N: This matches the calculated average force using F = Δp/Δt, and thus is the correct magnitude.
- 20,000 N: If this were the average force, the implied impulse would be 20,000 × 15 = 300,000 kg·m/s, which is inconsistent with the required Δp of 24,000 kg·m/s, so this is not correct.

In summary, by applying the impulse-momentum relationship and the given stopping time, only 1,600 N satisfies the physics of stopping the car within 15 seconds.

SPHY001 Practice Quiz - Unit 08 | LA048

To stop a 960-kg car traveling at 25 m/s in a time of 15 s requires an average force of magnitude

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