A particle moves in a straight line with an acceleration a ms-2 at time 't' seconds where a = -1t2. When t = 1 the particle has a velocity of 3 ms-1. Find the velocity of the particle at t = 4 s.

a= dvdt = -1t2 ⇒ = ∫3vdv = -∫141t2dt⇒v-3 = [1t]4 = 14-1⇒ v = 3-34 = 94 = 2.25 m/s

A particle moves in a straight line with an acceleration a ms-2 at time 't' seconds where a = -1t2. When t = 1 the particle has a velocity of 3 ms-1. Find the velocity of the particle at t = 4 s.

a= dvdt = -1t2 ⇒ = ∫3vdv = -∫141t2dt⇒v-3 = [1t]4 = 14-1⇒ v = 3-34 = 94 = 2.25 m/s

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A particle moves in a straight line with an acceleration $a {ms}^{- 2} at time' t' seconds where a = - \frac{1}{t^{2}} . When t = 1 the particle has a velocity of 3 {ms}^{- 1} . Find the velocity of the particle at t = 4 s .$

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5.25 m/s

1.25 m/s

2.25 m/s

8.25 m/s

answer is C.

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Detailed Solution

a= $\frac{dv}{dt} = \frac{- 1}{t^{2}} \Rightarrow = \int_{3}^{v} dv = - \int_{1}^{4} \frac{1}{t^{2}} dt$

$\Rightarrow v - 3 = {[\frac{1}{t}]}^{4} = \frac{1}{4} - 1$

$\Rightarrow v = 3 - \frac{3}{4} = \frac{9}{4} = 2.25 m / s$

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A particle moves in a straight line with an acceleration a ms-2 at time 't' seconds where a = -1t2. When t = 1 the particle has a velocity of 3 ms-1. Find the velocity of the particle at t = 4 s.

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A particle moves in a straight line with an acceleration $a {ms}^{- 2} at time' t' seconds where a = - \frac{1}{t^{2}} . When t = 1 the particle has a velocity of 3 {ms}^{- 1} . Find the velocity of the particle at t = 4 s .$