An automobile of mass 2000 kg moving at 20 m/s is braked suddenly with a constant braking force of 10,000 N. How far does the car travel before stopping?

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BlackTom AI · Accepted Answer

Consider the scenario: a car of mass m = 2000 kg is moving with initial speed v0 = 20 m/s and experiences a constant braking force F = 10,000 N opposite to its motion. The first step is to find the deceleration a produced by this force using Newton's second law: a = F/m = 10,000 N / 2000 kg = 5 m/s^2 (negative since it acts to slow the car).

Next, use the SUVAT (kinematics) relation that links initial velocity, final velocity, acceleration, and distance: v^2 = v0^2 + 2 a s. Since the car comes to rest, v = 0, so 0 = (20)^2 + 2(-5) s. This simplifies to 0 = 400 - 10 s, giving s = 400/10 = 40 m.

Now evaluate each option:
- 80 m: This would require a deceleration of a = v0^2/(2s) = 400/(160) = 2.5 m/s^2, which does not match the given braking force (a should be 5 m/s^2). Therefore this is inconsistent with the scenario.
- 40 m: This matches the derived distance using a = 5 m/s^2 and the work-energy/kinematics relation; the numbers align with the force and mass provided.
- None of these: Since 40 m is consistent with the calculation, this option is incorrect.
- 120 m: This would correspond to a much smaller deceleration (a = v0^2/(2s) = 400/(240) ≈ 1.667 m/s^2), which contradicts F = 10,000 N for m = 2000 kg.
- 180 m: This would imply an even smaller deceleration (a ≈ 400/(360) ≈ 1.111 m/s^2), again not matching the given braking force.

In summary, the distance required to stop under the stated constant braking force is determined by the deceleration a = F/m = 5 m/s^2 and the stopping condition v = 0, leading to s = v0^2/(2a) = 400/(10) = 40 m. The only option consistent with these calculations is 40 m, while all other distances imply decelerations that do not correspond to the provided force and mass.

2025 Fall PHYS 2205 TR 11:00 - 12:15 _ 89122 2205 Final Exam

An automobile of mass 2000 kg moving at 20 m/s is braked suddenly with a constant braking force of 10,000 N. How far does the car travel before stopping?

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