Car Braking Distance: Calculating Distance to Avoid Collision

[alex81388]

Homework Statement

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?

Homework 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

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?

Thanks in advance for all your help!

 

[Janvier]

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

Also, have you covered frames of reference?

 

[alex81388]

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

 

[alex81388]

Actually your diagram did help. Very good Advice.

I realized that as my chasing car was decelerating to the forward car's speed, the forward car was in fact still moving so its extra distance had to be accounted for (or in fact, discounted for).

My answer of 257.813 - 62.5 [the distance the forward car went in 15.625 seconds] = 195.313meters and is correct.

Thank you very much for your help :)