Kinetic energy

A car traveling at a speed of 25 km/h increased the speed to a) 75 km/h b) 100 km/h when exiting the highway. How many times has its kinetic energy increased?

Correct answer:

a =  9
b =  16

Step-by-step explanation:

$$\begin{gathered} v_1=25\text{km/h} \\ {v}_2=75\text{km/h} \\ {v}_3=100\text{km/h} \\ E=\frac{1}{2}m{v}^2 \\ E=K{v}^2 \\ a=\frac{E_2}{E_1}=\frac{K{v}_2^2}{K{v}_1^2} \\ a=\frac{v_2^2}{v_1^2}=\frac{75^2}{25^2}=9 \end{gathered}$$

$b=\frac{v_3^2}{v_1^2}=\frac{100^2}{25^2}=16$

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