If the velocity v of a particle moving along a straight line decreases linearly with its position coordinates s from 50m/s to a value approaching zero at = 100 m, the time it takes to reach the 100 m position will be:

Options

A. 10 s
B. 5 s
C. 0.5 s
D. infinity

Answer

D

Explanation

` v= 50(1-(s)/(100)) =50 -s//2m//s `
` rArr " "(ds)/(dt) =50 -s//2 rArr int _0^(s) (ds)/(50-s//2) =int _0^(t) dt `
` rArr " "-2l n [(50-s//2)/(50)] =trArr s=100( 1-e^(-t//2))`