Answer
(a) The maximum speed is 1.8 m/s.
The maximum speed is 4.0 mi/h.
(b) The acceleration is $180~m/s^2$, which is 18.4 g.
The force exerted on the head is 900 N.
Work Step by Step
(a) $E = \frac{1}{2}mv^2 = 8.0~J$
$v^2 = \frac{16.0~J}{m}$
$v = \sqrt{\frac{16.0~J}{5.0~kg}}$
$v = 1.8~m/s$
The maximum speed is 1.8 m/s.
We can convert this speed to mi/h.
$v = (1.8~m/s)(\frac{3600~s}{1~h})(\frac{1~mi}{1609~m})$
$v = 4.0~mi/h$
The maximum speed is 4.0 mi/h.
(b) $a = \frac{v}{t} = \frac{1.8~m/s}{0.010~s}$
$a = 180~m/s^2$
$a = \frac{180~m/s^2}{9.80~m/s^2} = 18.4~g$
The acceleration is $180~m/s^2$, which is 18.4 g.
We can find the force exerted on the head.
$F = ma = (5.00~kg)(180~m/s^2)$
$F = 900~N$
The force exerted on the head is 900 N.