Question

The friction coefficient between an athlete's shoes and the ground is $0.90$. Suppose a superman wears these shoes and races for $50$m. There is no upper limit on his capacity of running at high speeds. Suppose he takes exactly this minimum time to complete the $50$m, what minimum time will he take to stop?

Answer 1

Let the maximum acceleration be a.

$ma-\mu R=0$

$ma=\mu mg$

$a=\mu g=0.9\times 10=9m/sec$

$initialvelocity=u=0m/sec$

$t=?$

$a=9m/se{c}^2$

$s=5m$

$froms=ut+\frac{1}{2}\times a{t}^2$

$50=0+\frac{1}{2}a{t}^2$

$t=\frac{100}{9}$

$t=\frac{10}{3}sec=3.3sec$

AFTER MOVING $50m$, velocity of the athelete given by :

$V=u+at=0+9\times \frac{10}{3}$

he has to stop in minimum time, so deceleration is

$-a=-9m/se{c}^2$

$R=mg$

$ma=\mu R$

$a=\mu g=9m/se{c}^2\left(deceleration\right)$

${\mu }_1=30m/sec$

$v_1=0m/sec\times t=\frac{v_1-u_1}{a}$

$t=0-\frac{30}{-9}$

$t=\frac{10}{3}sec=3.3sec$