A car moving at a velocity of 20 m/s is behind a truck moving at a constant velocity of 18 m/s.When the car is 50 m behind the front of the truck,the car accelerates uniformly at 1.8 m/s2.The car continues at the same acceleration until it reaches a velocity of 25 m/s,which is the legal speed limit.The car then continues at a constant velocity of 25 m/s,until it passes the front of the truck.The distance the car travels while accelerating,in meters,is closest to:
A)50
B)54
C)58
D)62
E)66

Question

Quizplus · Accepted Answer

Let's first find the time it takes for the car to reach a velocity of 25 m/s:

v = u + at
25 = 20 + 1.8t
t = 2.78 seconds

During this time, the car travels a distance of:

s = ut + 0.5at^2
s = 20(2.78) + 0.5(1.8)(2.78)^2
s = 62.19 meters

Therefore, the distance the car travels while accelerating is closest to 62 meters, which is answer choice D.

A Car Moving at a Velocity of 20 M/s Is