Question

PLEASE ANS THIS QUESTION, ITS URGENT.....
The force of resistance on an object moving through a fluid is proportional to the
square of its velocity. The initial velocity of an object of mass 1 kg moving through the
fluid is 40 ms−1. After 5 s the velocity reduces to 20 ms−1. Calculate its velocity after 10 s.

Answer 1

The velocity after 10 seconds will be 13.33 m/s

Explanation :

Given, the force is directly proportional to velocity square

=> F = -kv²

=> ma = -kv²

=> mdv/dt = -kv²

=> dv/v² = -(k/m)dt

Integrating both the sides,

-1/v = (-kt/m)  + c

putting the given condition in the above equation we get,

at t = 0, v = 40 m/s

=> -1/40 = 0 + c

=> c = -1/40

at t = 5 , v = 20 m/s

=> -1/20 = (-5k/1) -1/40

=> -5k = -1/40

=> k = 1/200

putting these vale in the equation we get, at t = 10 s

-1/v = -(10/200x1) - 1/40

=> -1/v = -1/20 - 1/40

=> -1/v = -3/40

=> v = 40/3 = 13.33 m/s

Hence the velocity after 10 seconds will be 13.33 m/s