Question

The tangential acceleration of a particle moving in a circular path of radius 2m starting from rest varies with time as $a_t=3tm{s}^{-2}$ . The centripetal acceleration $\left(inm{s}^{-2}\right)$ of the particle at t=2s is:

• A. 12
• B. 18
• C. 16
• D. None of these

Answer 1

The correct option is B

18

$a_t=3t\frac{dv}{dt}=3t\Rightarrow {\int }_0^{v}dv=3{\int }_0^{2}tdtv=\frac{3t^2}{2}=6m{s}^{-1}{a}_c=\frac{v^2}{R}=\frac{6^2}{2}=18m{s}^{-2}$