# Homework Help: Question regarding motion of vehicles

1. Sep 24, 2009

### kitty89

1. Question:

You are driving your car (take the direction to be positive) at 20m/s. A van is following you, also at 20m/s. When you see a fog bank ahead of you, you hit the brakes (take this to be the time t=0). The driver of the van sees your brake lights and applies her brakes 1 second later. Both you and the van, when braking, have a constant acceleration of 5m/s^2 magnitude until coming to a stop.

After the van and the car have both stopped, are they further apart, closer together, or the same distance apart than at t=0? How much, in meters, has the distance between them changed?

How far behind the car should the van be at t=0 to avoid a collision?

2. Relevant equations:

Area under the graph of velocity versus time = distance travelled
s=s(initial)+v(initial)*t+(0.5)(a)(t^2)

3. The attempt at a solution

The van and the car are further apart after stopping.
Distance travelled by car after t=0:
(0.5)(4^2)(-5)=40m
Distance travelled by van after t=0:
(4)(20)+(0.5)(-5)(4^2)+20=60m
Change in distance=60m-40m=20m

The car and the van have to be at least 20m apart to avoid collision.

p/s: Is this correct? Thank you very much! =)
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution