A body of mass 2 kg travels according to the law x(t) =pt+qt2+rt3 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

Question

A body of mass 2 kg travels according to the law x(t) =pt+qt2+rt3 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 (B) 134 N (C) 158 N (D) 68 N

Tardigrade Admin · Accepted Answer

Here, x(t) =pt+qt2+rt3 where p=3 m s-1, q=4 m s-2, r=5 m s-3 and m=2 kg Velocity, v=(d x/d t)=(d/d t) (pt+qt2+rt3)=p+2qt+3rt2 Acceleration, a=(d v/d t) =2q+6rt At t=2 s, a=2 (4 m s-2) +6(5 m s-3)(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=ma =(2 kg)(68 m s-2) =136 N

Q. A body of mass $2 k g$ travels according to the 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 $t = 2$ seconds is

$136 N$

$134 N$

$158 N$

$68 N$

Q. A body of mass 2kg travels according to the 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=2 seconds is

136N

134N

158N

68N

Here, x(t) =pt+qt2+rt3 where p=3ms−1, q=4ms−2, r=5ms−3 and m=2kg Velocity, v=dtdx​=dtd​ (pt+qt2+rt3)=p+2qt+3rt2 Acceleration, a=dtdv​ =2q+6rt At t=2s, a=2 (4ms−2) +6(5ms−3)(2s) =8ms−2+60ms−2=68ms−2 The force acting on the body of mass 2kg is F=ma =(2kg)(68ms−2) =136N

Q. A body of mass $2 k g$ travels according to the 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 $t = 2$ seconds is

$136 N$

$134 N$

$158 N$

$68 N$