# Differentiation car problem

1. Dec 7, 2007

### jnimagine

1. The problem statement, all variables and given/known data
A car, travelling at a speed of 90km/h, approaches a stop sign 40m ahead. If the car immediately begins to decelerate at a rate of -8m/s^2, will it be able to stop in time? Justify your response

2. Relevant equations
d = 1/2at^2 + vt

3. The attempt at a solution

I found time by doing t = v/a and found it to be 25/8s
Then I subbed it in d = 1/2at^2 + vt and got an answer of 39.1m, which is smaller than 40m. So it will be able to stop in time.
But this assignment is all about differentiation, so I should be finding a derivative somewhere.... but I don't know where to find a derivative to solve this problem!!

2. Dec 7, 2007

### dotman

Hello,

Well, you've kind of already used differentiation, but you may not know it. You have an equation for position:

$$x(t) = x_0 + v_0t + \frac{1}{2}at^2$$

The velocity is found by taking the derivative of this equation:

$$v(t) = \frac{dx}{dt} = v_0 + at$$

So when you calculated your time (where did you get t = v/a?) you were using this equation.

Hope this helps.