# Car braking distance

1. Jan 15, 2008

### alex81388

1. The problem statement, all variables and given/known data
A certain automobile can decelerate at |a1| = 1.6 m/s2. Traveling at a constant v1 = 29 m/s, this car comes up behind a car traveling at a constant v2 = 4 m/s. How close to the slower car can the driver of the faster car come before applying his brakes and still avoid a collision?

2. Relevant equations

V(final)^2 - V(initial)^2 = 2a(X(final)-X(initial))
X = X(initial) + V[initial]*t + .5(a)(t^2)
V[final] = V[initial] + at

3. The attempt at a solution

First thing we need is to solve for the time needed to for the application of the braking system:

V[final] = V[initial] + at
4 = 29 + (-1.6)(t)
t = 15.625

X = X(initial) + V[initial]*t + .5(a)(t^2)
x = 0 + (29)(15.625) + .5(-1.6)(15.625^2)
x=257.8

So I decided the answer was 257.8 meters. This however is not correct. What am I doing wrong?

2. Jan 15, 2008

### Janvier

Have you drawn a diagram yet? I think if you did, it would be very helpful.

Also, have you covered frames of reference?

Last edited: Jan 15, 2008
3. Jan 15, 2008

### alex81388

I have not yet covered frames of reference. I tried drawing a diagram and the thought process still makes sense to me.

4. Jan 15, 2008