# A ball has a mass of 4.0 kg and is moving with a velocity of 15.0 km/h. The ball increased its speed to 30.0 Km/h, then the K.E of the ball will ?

Nov 26, 2017

OK, we need to find initial KE, final KE and the ratio between them (must be > 1) We’d normally have to start by putting velocity into SI units, but as we’re only after a ratio it won’t matter.

#### Explanation:

$K {E}_{1} = \frac{1}{2} m . {v}^{2} = \frac{1}{2} \times 4 \times {15}^{2}$

$K {E}_{1} = 450$J

$K {E}_{2} = \frac{1}{2} m . {v}^{2} = \frac{1}{2} \times 4 \times {30}^{2}$

$K {E}_{2} = 1800$J

The KE has thus gone up by a factor of $\frac{K {E}_{2}}{K {E}_{1}} = \frac{1800}{450}$ = 4.

So when velocity doubles, KE goes up by the square of that (in the equation there is a ${v}^{2}$ term) and ${2}^{2} = 4$ times.