Constant acceleration: A car is 200 m from a stop sign and traveling toward the sign at 40.0 m/s. At this time, the driver suddenly realizes that she must stop the car. If it takes 0.200 s for the driver to apply the brakes, what must be the magnitude of the constant acceleration of the car after the brakes are applied so that the car will come to rest at the stop sign? A) 2.89 m/s² B) 3.89 m/s² C) 4.17 m/s² D) 3.42 m/s² E) 2.08 m/s²

Question

Quizplus · Accepted Answer

The distance the car travels during the reaction time is:
d = v₀t + ½at²
d = (40.0 m/s)(0.200 s) + ½a(0.200 s)²
d = 4.00 m + 0.02a

To come to a stop, the car must travel a distance of 200 m, so the total distance traveled is:
d = 4.00 m + 0.02a + 200 m

Setting the total distance equal to the distance formula:
200 m = ½at² + v₀t

Substituting the initial velocity and rearranging, we get:
a = (2d - 2v₀t) / t²
a = (2(200 m) - 2(40.0 m/s)(0.200 s)) / (0.200 s)²
a = 4.17 m/s²

Therefore, the magnitude of the constant acceleration of the car after the brakes are applied needs to be 4.17 m/s². So, the correct answer is C.

Constant Acceleration: a Car Is 200 M from a Stop