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  • A body of mass 2kg travels according to the law x(t ) = pt + qt^2 + rt^3 where p = 3 ms^-1, q = 4 ms^-2 and r = 5 ms^-3. The force acting on the body at t = 2 seconds is (a) 136 N

A body of mass 2kg travels according to the law x(t ) = pt + qt^{2} + rt^{3} where p = 3 ms^{-1}, q = 4 ms^{-2} and r=5ms^{-3}. The force acting on the body at t = 2 seconds is
(a) 136 N
(b) 134 N
(c) 158 N
(d) 68 N

Answers (1)

The answer is the option (a) 136N

Explanation:

x(t ) = pt + qt^{2} + rt^{3} 

p = 3 ms^{-1}, q = 4 ms^{-2}  r=5ms^{-3}

x(t) = 3t + 4t^{2} + 5t^{3}

 thus, \frac{dx(t)}{dt } = 3 + 8t + 15t^{2}

\frac{d^{2}x(t)}{dt^{2}}=0+8+30t

\left [\frac{d^{2}x(t)}{dt^{2}} \right ]_{t=2}=8+30\times 2=68ms^{-2}

 Now, we know that,

\overrightarrow{F}=m\overrightarrow{a}=m.\frac{d^{2}x}{dt^{2}}

Thus,

\overrightarrow{F}=2 \times 68

  =136\ N

Posted by

infoexpert24

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