A body of mass2kg travels according to thel aw $x (t) = p t + q r^{2} + r t^{3}$ , where p = 3m/s ,q = $4 m s^{- 2}$ and $r = 5 m s^{- 3}$ .The force acting on the body at t=2seconds is:

136N

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134N

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158N

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68N

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Solution

The correct option is A 136N
First we have to calculate acceleration and then Newton's second law will be applied.

Given :-

Mass of the body = m = 2Kg

Time = t = 2 s

Position of Particle x(t) = pt + qt² + rt³

Where,

p = 3 ms-¹

q = 4 ms-²

r = 5 ms-³

Putting this and Differentiating w.r.t 't' in order to get Velocity

v = dx/dt
v = d(3t + 4t² + 5t³)/dt
v = 3 + 8t + 15t²

Again Differentiating 'V' w.r.t 't' in order to get acceleration.
a = dv/dt
a = d(3 + 8t + 15t²)/dt
a = 8 + 30t
a = 8 + 30 × 2
a = 68 ms-¹

As we know that,
F = ma
F = 2(68)
F = 136 N
Hence,Force acting on the body = F = 136 N.

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