# Kinetic Energy speed and a car

1. Apr 21, 2005

### fizz123

One car has twice the mass of a second car, but only half as much kinetic energy. When both cars increase their speed by 8.5 m/s, they then have the same kinetic energy. What were the original speeds of the two cars?

first i set it up like this:
.5 * m * v1^2 = .5 * (.5 * 2m * v2^2)

then i get:
v1 = v2

then
.5 * m * (v1 + 8.5)^2 = .5 * 2m * (v2 + 8.5)^2
.5 * (v1 + 8.5)^2 = (v2 + 8.5)^2

but its not right...

2. Apr 21, 2005

### arildno

1) "One car has twice the mass of a second car" $$m_{1}=2m_{2}$$
2) "but only half as much kinetic energy" $$K_{1}=\frac{K_{2}}{2}$$
3)"When both cars increase their speed by 8.5 m/s, they then have the same kinetic energy":
$$\frac{m_{1}}{2}(v_{1}+8.5)^{2}=\frac{m_{2}}{2}(v_{2}+8.5)^{2}, K_{1}=\frac{m_{1}}{2}v_{1}^{2},K_{2}=\frac{m_{2}}{2}v_{2}^{2}$$

$$K_{1}=\frac{2m_{2}}{2}v_{1}^{2}=\frac{m_{2}}{4}v_{2}^{2}=\frac{K_{2}}{2}$$

Thus, we have: $${v}_{1}=\frac{v_{2}}{2}$$

Last edited: Apr 21, 2005
3. Apr 24, 2005

### fizz123

thank you, i got it now

4. Feb 2, 2010

### tigerwoods99

Howcome both masses are over 2?