Question

A body of mass 2 kg travels according to the law x(t) = pt + $qt^{2} + rt^{3}$ 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. 134N
• C. 158 N
• D. 68 N

Answer 1

Answer: (A)

136 N

Answer 2

Here $x(t) = pt + qt^{2} + rt^{3}$

Where $p = 3ms^{- 1}m,q = 4ms^{- 2}andr = 5ms^{- 2}$

M=2kg

Velocity , $v = \frac{dx}{dt} = \frac{d}{dt}(pt + qt^{2} + rt^{3}) = p + 2qt + 3rt^{2}$

Acceleration , $a = \frac{dv}{dt} = 2q + 6rt$

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 2 kg is

$F = ma = (2kg)(68ms^{- 2}) = 136N$