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A body of mass $10 kg$ is being acted upon by a force $3 t^{2}$ and an opposing constant force of $32 N$ . The initial speed is $10 {ms}^{- 1}$ . The velocity of body after $5 s$ is

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$14.5 {ms}^{- 1}$

$6.5 {ms}^{- 1}$

$4.5 {ms}^{- 1}$

$3.5 {ms}^{- 1}$

answer is B.

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Detailed Solution

$F = 3 t^{2} - 32 a = \frac{F}{m} = (0.3 t^{2} - 3.2) \int_{10}^{v} d v = \int_{0}^{5} a d t = \int_{0}^{5} (0.3 t^{2} - 3.2) d t v - 10 = - 3.5 ∴ v = 6.5 m / s$

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