Question

The friction coefficient between an athlete's shoes and the ground is 0.90. Suppose a superman wears these shoes and and races for 50 m. There is no upper limit on his capacity of running at high speeds. (a) Find the minimum time 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

Answer 1

(a). If we want to find the minimum time, then Limiting Friction must be equal to the force applied.

⇒ friction = ma

⇒ μmg = ma

⇒ a = 0.9 × 10

⇒ a = 9 m/s².

Now, u = 0

∴ S = ut + 1/2 × at²

⇒ 50 = 0 + 1/2 × 9 × t²

⇒ t² = 100/9

⇒  t = 10/3

∴ t = 3.33 seconds.

(b). It will also be same as the time for completing, means answer will be same as 3.33 seconds.

Hope it helps .