Question

A body of mass $10$ kg is being acted upon by a force $3t^2$ and an opposing constant force of $32N$. The initial speed is $10m{s}^{-1}.$ The velocity of body after $5s$ is:

• A. $14.5m{s}^{-1}$
• B. $6.5m{s}^{-1}$
• C. $3.5m{s}^{-1}$
• D. $4.5m{s}^{-1}$

Answer 1

The correct option is B $6.5m{s}^{-1}$

$F=ma$
$\therefore 10a=3t^2-3210\frac{dv}{dt}=3t^2-3210{\int }_{10}^{v}dv={\int }_0^5{(3t}^2-32)dt10v-100=5^3-32\times 510v=100-35v=6.5m/s$