Math Help - Antiderivative deceleration problem.

1. Antiderivative deceleration problem.

PLEASE NO PHYSICS FORMULAS: I AM TRYING TO SOLVE THIS USING THE INTEGRAL AND THE MVT. THANKS.

A car is traveling at 100 km/h when the driver sees an accident 80 m ahead and slams on the breaks. What constant deceleration is required to stop the car in time to avoid a pileup?

What I think I know:

I am looking for : a(t)=(v2-v1)/t

Where: v1=initial velocity=100 km/h
v2=terminal velocity=0 km/h
t=time= unknown.

But first I need to find where s(t)=80m in order to find the time.

This is where I seem to be stuck...do I take the first Integral of a(t) or the second and use it as s(t)? Or is there something else I'm missing?

2. Re: Antiderivative deceleration problem.

We have

$\frac{dv}{dt}=A=const$

$dv(t)=A\;dt$

Integrating we get

$\int_0^t{dv(t)}=\int_0^t{A \; dt}$

$v(t)-v(0)=At$

$v(t)=v(0)+At$

Now you may go on:

$\frac{dS}{dt}=v(t)$