Question

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

• A. 136 N
• B. 134 N
• C. 158 N
• D. 68 N

Answer 1

Answer: (A)

Given, $x(t)=p t+q t^{2}+r t^{3}$ and $p=3 \,ms ^{-1}, q=4 \,ms ^{-2}$,
$r=5 \,ms ^{-3}$, then $x(t)=3 t+4\, t^{2}+5 \,t^{3}$
$a=\frac{d^{2} x(t)}{d t^{2}}=8+30\, t $
$\therefore t=2 \,s$
$\therefore a=8+30 \times 2=68$
Now $F=m \times a=2 \times 68=136\, N$