A body of mass `m`, moving along the positive x direction is subjected to a resistive force `F = Kv^(2)` (where K is a constant and `v` the particle n velocity). If `m = 10 kg v = 10 m//s` at `t = 0, " and " K = 2N (m//s)^(-2)` the velocity when `t = 2s` is:A. `(10)/(3) m//s`B. `2 m//s`C. `- (10)/(3) m//s`D. `(3)/(10) m//s`

A body of mass `m`, moving along the positive x direction is subjected

1.	A body of mass `m`, moving along the positive x direction is subjected to a resistive force `F = Kv^(2)` (where K is a constant and `v` the particle n velocity). If `m = 10 kg v = 10 m//s` at `t = 0, " and " K = 2N (m//s)^(-2)` the velocity when `t = 2s` is:A. `(10)/(3) m//s`B. `2 m//s`C. `- (10)/(3) m//s`D. `(3)/(10) m//s`
Answer» Correct Answer - B `F = - k v^(2)` `m (dv)/(dt) = - kv^(2)` `underset(10)overset(v)int (dv)/(v^(2)) = - (k)/(m) underset(0)overset(t)int dt` `- \|(1)/(v)\|_(10)^(v) = (2)/(10) \|t\|_(0)^(t)` `(1)/(v) - (1)/(10) = (1)/(5) (2)` `v = 2 m//s`

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