# Given distance and acceleration, find time

ScienceGirl90

## Homework Statement

A car is moving at 50.0 m/s and brakes to a halt in 6.00 seconds.
How long does it take the car to travel 70.0 m after the car starts decelerating?

a=dv/dt
t=??

## The Attempt at a Solution

I'm pretty sure I know how to find the acceleration but I'm confused as to how to set up an equation to find the time.

## Answers and Replies

Lancelot59
Simple. Use a kinematics equation that has all the variables you need in it. Think about it. You know initial velocity, the distance it travels, and the acceleration. You need to find time. Which formula has all of those variables in it? Let me know if you haven't been given those formulae, and I can give you hints on how to solve it the long way.
The acceleration is simple, remember the basic equation:

$$a=\frac{V_{Final} - V_{Initial}}{\Delta Time}$$

ScienceGirl90
For the acceleration I got -8.33 m/s2

Then for the time, do I use the equation:
x=1/2*a*t2+Vo*t

When I tried using that equation I was left with two 't' variables and couldn't get it down to one.

Lancelot59
For the acceleration I got -8.33 m/s2

Then for the time, do I use the equation:
x=1/2*a*t2+Vo*t

When I tried using that equation I was left with two 't' variables and couldn't get it down to one.

Correct formula. However take a look at this, you have d=(stuff)t2+(stuff)t. What kind of function does that look like?

ScienceGirl90
It looks like a quadratic function? I don't know how to get it to t='stuff'

Lancelot59
You don't. You wanna get t correct? Well there happens to be this thing called the quadratic formula that will solve for your quadratic variable (t in this case), where the equation is equal to zero.

ScienceGirl90
Oh I see! Thank you very much!

Lancelot59
You're welcome. Let me know how that works out. You should start with:

(stuff)t2+(stuff)t-d=0 and then plug that in.