Two cars are traveling along a straight line in the same direction, the lead car at 26 m/s and the other car at 40 m/s. At the moment the cars are 49 m apart, the lead driver applies the brakes, causing the car to have a deceleration of 1.5 m/s^2. How long does it take for the lead car to stop? Answer in units of s. (52/3)

Question

032 (part 2 of 3) 10.0 points
Assume that the driver of the chasing car applies the brakes at the same time as the driver of the lead car. What must the chasing car’s minimum negative acceleration be to avoid hitting the lead car? Answer in units of m/s^2.

How long does it take the chasing car to
stop? Answer in units of s

Answer 1

1. t = (Vf - Vo) / a,
t = (0 - 26) / -1.5 = 17.33s.

d = (Vf^2 - Vo^2) / 2a,
d = (0 - (26)^2) / -3 = 225.33m = stopping distance for lead car.

d = 49 + 225.33 = 274.33m = Required stopping distance for the chasing car.

a = (Vf^2 - Vo^2) / 2d,
a = (0 - (40)^2) / 548.66 = -2.92m/s^2.
= required deceleration of 2nd car.

t = (Vf - Vo) / a,
t = (0 - 40) / -2.92 = 13.72s. = Time it takes for the 2nd car to stop.