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

The correct answer is 136 N.

Step 1: Identify the given values
We are given the following properties of the traveling body:
- Mass of the body, $m=2\text{kg}$
- Position function, $x\left(t\right)=pt+q{t}^2+r{t}^3$
- Constant parameters: $p=3{\text{ms}}^{-1}$, $q=4{\text{ms}}^{-2}$, and $r=5{\text{ms}}^{-3}$
- Time, $t=2\text{s}$

Step 2: Find the velocity function by differentiating the position with respect to time
$v\left(t\right)=\frac{dx}{dt}=\frac{d}{dt}(pt+q{t}^2+r{t}^3)$

$v\left(t\right)=p+2qt+3r{t}^2$

Step 3: Find the acceleration function by differentiating the velocity with respect to time
$a\left(t\right)=\frac{dv}{dt}=\frac{d}{dt}(p+2qt+3r{t}^2)$

$a\left(t\right)=2q+6rt$

Step 4: Calculate the acceleration at t = 2 seconds
Substitute the values $q=4$, $r=5$, and $t=2$ into the acceleration equation:
$a\left(2\right)=2\left(4\right)+6\left(5\right)\left(2\right)$

$a\left(2\right)=8+60=68{\text{ms}}^{-2}$

Step 5: Calculate the force acting on the body
Using Newton's second law of motion ($F=m\cdot a$):
$F=2\text{kg}\times 68{\text{ms}}^{-2}=136\text{N}$