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Electric Field

A body of mas...

Question

A body of mass 2 kg travels according to the law $x (t) = p t + q t^{2} + r t^{3}$ where $p = 3 m s^{- 1}, q = 4 m s^{- 2}$ and $r = 5 m s^{- 3}$ . The acting on the body at t=2 seconds is

136 N

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134 N

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158 N

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68 N

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Solution

The correct option is A 136 N
Here, $x (t) = p t + q t^{2} + r t^{3}$
Where $p = 3 m s^{- 1}, q = 4 m s^{- 2}, r = 5 m s^{- 3}$ and m=2 kg

Velocity, $v = \frac{d x}{d t} = \frac{d}{d t} (p t + q t^{2} + r t^{3}) = p + 2 q t + 3 r t^{2}$

Acceleration, $a = \frac{d v}{d t} = 2 q + 6 r t$

At $t = 2 s, a = 2 (4 m s^{- 2}) + 6 (5 m s^{- 2}) (2 s)$
= $8 m s^{- 2} + 60 m s^{- 2} = 68 m s^{- 2}$

The force acting on the body of mass 2 kg is
$F = m a = (2 k g) (68 m s^{- 2}) = 136 N$

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