A body of mass 2 kg travels according to law x(t)=p t+q t2+r t3, 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

Question

A body of mass 2 kg travels according to law x(t)=p t+q t2+r t3, 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

Tardigrade Admin · Accepted Answer

Given, x(t)=p t+q t2+r t3 and p=3 ms -1, q=4 ms -2, r=5 ms -3, then x(t)=3 t+4 t2+5 t3 a=(d2 x(t)/d t2)=8+30 t ∴ t=2 s ∴ a=8+30 × 2=68 Now F=m × a=2 × 68=136 N

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

136 N

134 N

158 N

68 N

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

Q. A body of mass 2kg travels according to law x(t)=pt+qt2+rt3, where p=3ms−1,q=4ms−2 and r=5ms−3. The force acting on the body at t=2s is