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

Given, mass = 2kg
`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 + `6 xx 2 xx r`
`= 2q + 12r`
` = 2 xx 4 + 12 xx 5`
` = 8 + 60 = 68 m//s`
Force (F) = ma
` = 2 xx 68 = 136 N`