# Homework Help: The maximum deceleration of a car

1. Jan 24, 2010

### Judas543

The maximum deceleration of a car....

1. The problem statement, all variables and given/known data
The maximum deceleration of a car on a dry road is about 8.0 m/s^2

3. 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?

B)
How far apart will they be when they stop?

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 [Broken]

Last edited by a moderator: May 4, 2017
2. Jan 24, 2010

### xcvxcvvc

Re: The maximum deceleration of a car....

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.