The maximum deceleration of a car

[Judas543]

The maximum deceleration of a car...

Homework Statement

The maximum deceleration of a car on a dry road is about 8.0 m/s^2

The Attempt at a Solution

A)
If two cars are moving head-on toward each other at 88 km/h (55 mi/h), and their drivers apply their brakes when they are 85 m apart, will they collide?
Answer: No


B)
How far apart will they be when they stop?
Answer: 10m


C) HELP Drawing the graph and points

On the same graph, plot distance versus time for both cars.
Assume x = 0 is the midpoint between the cars and t = 0 when the brakes are applied. Label the position versus time plot of the car with the positive velocity as x_1(t).
http://img684.imageshack.us/img684/6803/94527989.png

 

[xcvxcvvc]

if x = 0 is the midpoint, car 1 is at x = -85/2 and car 2 is at 85/2 initially.

x(t) = 1/2 a t^2 + v * t + x(i)
so
x_1(t) = 1/2 (-8) * t^2 + 88000/3600 * t - 85/2
x_2(t) = 1/2 8 t^2 - 88000/3600 * t + 85/2
Notice that car 2's velocity is positive (to the right) and its acceleration is negative(to the left). The reverse is true for car 2.