Question

K = $\tfrac{1}{2} mv^2$. For a given mass, when speed is 2 m/s, K is 25 J, find the speed when K becomes 625 J.

• A. 10 m/s
• B. 5 m/s
• C. 4 m/s
• D. 25 m/s

Answer 1

Answer: (A)

10 m/s

Answer 2

Key concept: Kinetic energy $K = \tfrac12 m v^2$, so $K\propto v^2$.

1. At $v_1 = 2$ m/s, $K_1 = 25$ J.
2. At unknown $v_2$, $K_2 = 625$ J.

Using ratio:

$$\frac{K_2}{K_1} = \frac{v_2^2}{v_1^2} \;\Longrightarrow\; \frac{625}{25} = \frac{v_2^2}{(2)^2} \;\Longrightarrow\; 25 = \frac{v_2^2}{4} \;\Longrightarrow\; v_2^2 = 100 \;\Longrightarrow\; v_2 = 10\text{ m/s}.$$