Question

An object stars from rest at $t=0$ and accelerates at a rate given by $a=6t$. What i) its velocity and ii) its displacement at any time $t$?

• A. $t^3,3t^2$
• B. $3t^2,t^3$
• C. $t^2,t^3$
• D. $2t^2,3t^3$

Answer 1

The correct option is B $3t^2,t^3$

At $t=0$, $v=0$

$a=6t⟹\frac{dv}{dt}=6t⟹dv=6tdt$
on intersection, we get $⟹v=3t^2+c$

now, at $t=0,v=0$

So, $v=3t^2$

$v=3t^2⟹\frac{dx}{dt}=3t^2⟶dx=3t^{2}dt$

On intersection, we get

$S=t^3+c$

Now, at $t=0,S=0$

So, $S=t^3$

and $v=3t^2$