## College Physics (4th Edition)

The speed of the police car when it catches up to the speeder is $2v$
Let's suppose that the police car catches up to the speeder after a time $t$. The distance traveled by the speeder is $vt$. If the police car catches up to the speeder, the police car must also travel this same distance. We can find the police car's acceleration: $\Delta x = \frac{1}{2}at^2$ $vt = \frac{1}{2}at^2$ $a = \frac{2v}{t}$ We can find the police car's final velocity: $v_f = v_0+at$ $v_f = 0 + (\frac{2v}{t})(t)$ $v_f = 2v$ The speed of the police car when it catches up to the speeder is $2v$