Question

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 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? 3.89 m/s2 4.17 m/s2 2.89 m/s2 3.42 m/s2 2.08 m/s2

Answer 1

4.17 m/s²

Step-by-step explanation:

We are told the reaction time is 0.2 s. Now, during this reaction time the car is going to travel an additional distance of : x = u × t = 40 × 0.2 = 8 m

where u is the initial velocity of the car which is 40.0 m/s.

We are told that he had 200 m to stop before applying brakes. Thus, after applying brakes, he now has a distance to cover of; s = 200 - 8 = 192 m

Since vehicle is coming to rest acceleration would be negative, thus using Newton's equation of motion, we have;

v ² = u² - 2as

v = 0 m/s since it's coming to rest

u = 40 m/s

s = 192 m

Thus;

0² = 40² - 2(a)(192)

0² = 1600 - 384a

a = 1600/384

a = 4.17 m/s²