Question

A object starts from rest at $t=0$ and accelerates at a rate given by $a=6t$. What is its velocity?

• A. $6t$
• B. $3t^2$
• C. $6t^2$
• D. $0$

Answer 1

The correct option is B $3t^2$

Answer is B.
As acceleration is given as a function of time,

Therefore, $V={\int }_{t_0}^{t}a\left(t\right)dt$

So, ${\int }_0^{t}6tdt$

$\Rightarrow 6(\frac{t^2}{2}-0)=3t^2$

So, $V$ = $3t^2$

Hence, velocity v(t) = $3t^2$