Question

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

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

Answer 1

The correct option is D $6.5{ms}^{-1}$

Net force on the body is $F=3t^2-32$

so net acceleration will be $a=\frac{F}{m}=0.3t^2-3.2$

We know that acceleration is $a=\frac{dv}{dt}$ so $dv=adt$

integrating both sides we get ${\int }_{v=10}^{V}dv={\int }_{t=0}^{t=5}(0.3t^2-3.2)dt$

we get the new velocity after $5s$ as $V=10+\frac{0.3}{3}(5^3-0)-3.2(5-0)$

or $V=6.5m/s$