Problem 4- Speedy car, driving at 30 m/s. The driver suddenly observes a slow-moving van 155 m ahead traveling at 5 m/s in the same direction. The driver of the car immediately applies the brakes causing a constant acceleration of 2 m/s2 in a direction opposite to the cars velocity.

Question

a) After the driver of the car applies the brakes, at what time the car will collide with the van?
b) Take x= 0 at the location of the car when the brakes applied, where does the collide with the van?

Answer 1

if the collide, they have traveled the same distance in the same time.

distance van=155+5t
distancecar=30t-1/2 *2*t^2

set them equal, solve for time t.

then using t, solve for car distance.

Answer 2

t = 10.5 s