1-D (I think) Speed to distance problem

1. Feb 6, 2014

magnanimousto

1. The problem statement, all variables and given/known data

A runner exerts a constant force to accelerate from rest to 2.0 m/s over a distance of 12 m.
Assuming the runner can keep up the same force, what total distance would be needed to ac-
celerate up from rest to 3.0 m/s?

2. Relevant equations

none given.

3. The attempt at a solution

The answer to the problem is 27. After quite some time spent thinking I tried solving first part for time using x= 1/2 vt and then plugging it into 2nd part. but that gives time as 12 and 2nd x as 18 so wrong. Dunno how to solve it

2. Feb 6, 2014

SammyS

Staff Emeritus
Hello magnanimousto. Welcome to PF!

What kinematic equations do you know?

Alternatively, do you know the Work-Energy Theorem ?

3. Feb 6, 2014

jackarms

This is a constant acceleration problem, so you can use the basic kinematic equations for that case. Try solving for the acceleration first, and using that value for the next part.

If you don't know those equations, here's the one you should probably use -- they're very helpful to memorize though.
$v_{f}^{2}= v_{i}^{2} + 2aΔd$

4. Feb 7, 2014

magnanimousto

Thanks jackarms & SammyS.I do know kinematics equations, for some reason it never occurred to me that since the force is the same in both so must be the acceleration