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

Options

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

Answer

A

Explanation

(a) Given , mass =2 kg
`x(t)=pt+qt^(2)+rt^(3)`
`v=(dx)/(dt)=p+2qt+3rt^(2)`
`a=(dv)/(dt)=0+2q+6rt`
At` t=2s,a=2q+6xx2xxr=2q+12r`
=`2xx4+12xx5=8+60=68 ms^(-1)`
Force ,` F=ma=2xx68=136N`