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

Using the equation of motion:

d = Vit + 1/2at^2

where 
d = distance = 200 m (since the car needs to stop at the stop sign) 
Vi = initial velocity = 40 m/s (since the car is traveling towards the stop sign at 40 m/s) 
t = time = 0.2 s (since it takes 0.2 s for the driver to apply the brakes) 
a = acceleration (what we're supposed to find)

Plugging in the values:

200 = (40)(0.2) + 1/2(a)(0.2)^2

Simplifying, we get:

200 = 8 + 0.02a

192 = 0.02a

a = 9600/2

a = 4800 m/s^2

Therefore, 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 is 4.17 m/s^2 (choice C).

A Car Is 200 M from a Stop Sign and Traveling