Question

The acceleration $a$ (in ${ms}^{-2}$) of a body, starting from rest varies with time $t$ (in $s$) following the equation $a=3t+4$. The velocity of the body at time $t=2s$ will be

• A. $10{ms}^{-1}$
• B. $18{ms}^{-1}$
• C. $14{ms}^{-1}$
• D. $26{ms}^{-1}$

Answer 1

The correct option is C $14{ms}^{-1}$

Given $a=3t+4$
$\Rightarrow \frac{dv}{dt}=3t+4$
$\therefore {\int }_0^{v}dv={\int }_0^t(3t+4)dt$
$\Rightarrow v=\frac{3}{2}{t}^2+4t$
at $t=2s$
$v=\frac{3}{2}{\left(2\right)}^2+4\left(2\right)=14{ms}^{-1}$