Question

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

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

Answer 1

Answer: (B)

$6.5{ms}^{-1}$

Here, $ma=3t^2-32$
$10a=3t^2-32\Rightarrow a=\frac{dv}{dt}=0.3t^2-3.2$
Since acceleration is not constant, we need to integrate a to fins out v.
Integrating,
$v=\int 0.3t^{2}dt-3.2\int dt+C=\frac{1}{10}{t}^3-3.2t+C$
At $t=0$, $v=10$
$\Rightarrow 10=C$
$\Rightarrow v=\frac{1}{10}{t}^3-3.2t+10$
At $t=5$, $v=\frac{1}{10}{5}^3-3.2\times 5+10=12.5-16+10=6.5m/s$