The friction coefficient bettween an athelete's shoes and the ground is 0.90. Suppose a superman wears these shoes and races for 50 m. There is no upper limit in his capacity of running at high speeds. A. Find the minimum time that he will have to take in completing the 50 m starting from rest. b. Suppose he takes exactly this minimum time to complete the 50 m, what minimum time will he take to stop?

Explanation

To reach minimum time he has to move with mximum possible acceleration.
Let the maxium accelerationis a
`:. Ma-muR=0rarrma=mu mg `
`rarr a=mug=0.9xx10=9m/s^2`
a. Initial velocity,
u=0 t=? `
a=9m/s^2 S=50m
From the equation `S=ut+(1/2)at^2`
`50=0+(1/2)9t^2`
`rarr t=10/3 sec`
b. After covering `50m`, velocity of teh athelete is given by `
v=u+at`
`=0+9xx(10/3)m/s `
He has to stop in minimum time. so deceleration is `-a=-9m/s^2(max)`
`R=mg
`ma=muR`
(maximum frictioN/Al force)
`rarr a=mug`
`rarr =9m/s^2 (deceleration)`
`u_1=30 m/s,v=0`
`rarr t=(v_1-u_1)/a`
`=(0-30)/(-a)`
`=(-30)/(-a) =10/3 sec`