# Work-Energy Theorem / Finding The Mass

1. Nov 8, 2009

### crono_

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

It takes 241 kJ of work to accelerate a car from 22.0 m/s to 28.8 m/s. What is the car's mass?

W = 241000 J

vo = 22.0 m/s

vf = 28.8 m/s

m = ?

2. Relevant equations

KE = 1/2 mv2

W = KEf - KEo

3. The attempt at a solution

W = KEf - KEo

W = 1/2 mvf2 - 1/2 mvo2

I was trying to solve for m as everything else is known, but I think I got stuck somewhere in the algebra.

W = 1/2 (mvf2 - mvo2)

2W = mvf2 - mvo2

2W / vf2 - vo2 = m - m

That's as far as I got. I'm wondering if by switching the sides of the equation so that their signs would change if then m - m could become m + m, thus 2m. Then divide both sides by 2.

Does that seem right?

Thanks!

2. Nov 8, 2009

### jgens

$$2W = mv_f^2 - mv_i^2 = m(v_f^2 - v_i^2)$$

$$m = \frac{2W}{v_f^2 - v_i^2}$$

3. Nov 8, 2009

### crono_

Thank you! I completely overlooked that! :)

4. Nov 8, 2009

### jgens

You're welcome!