Question

A body of mass m = 10−2 kg is moving in a medium and experiences a frictional force f = −kv2 where v is the instantaneous velocity of the body . its initial speed is v0 = 10ms−1. if, after 10 s, its energy is 1 8mv2 0, the value of k will be

a. 10−3 kg m−1

b. 10−3 kg s−1

c. 10−4 kg m−1

d. 10−1 kg m−1 s−1

Answer 1

12mv2f=18mv20

vf=V02=5m/s

(10−2)dvdt=−kv2

∫105dvv2=−100k∫010dt

15−110=100k(10)

k=10−4