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Uniform Acceleration

The accelerat...

Question

The acceleration $a$ (in ${m s}^{- 2}$ ) of a body, starting from rest varies with time $t$ (in $s$ ) following the equation $a = 3 t + 4$ . The velocity of the body at time $t = 2 s$ will be

10 {m s}^{- 1}

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18 {m s}^{- 1}

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14 {m s}^{- 1}

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26 {m s}^{- 1}

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Solution

The correct option is C $14 {m s}^{- 1}$
Given $a = 3 t + 4$
$\Rightarrow \frac{d v}{d t} = 3 t + 4$
$∴ \int_{0}^{v} d v = \int_{0}^{t} (3 t + 4) d t$
$\Rightarrow v = \frac{3}{2} t^{2} + 4 t$
at $t = 2 s$
$v = \frac{3}{2} {(2)}^{2} + 4 (2) = 14 {m s}^{- 1}$

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