Question

A point moves along a circle having a radius $20$ cm with a constant tangential acceleration $5m/s^2$. How much time is needed, after motion begins, for the normal acceleration of the point to become equal to tangential acceleration?

Answer 1

Normal acceleration $a_n=\frac{v^2}{r}=\frac{dv}{dt}=a_t=5\Rightarrow v^2=5\times r=5\times 0.2=1\Rightarrow v=1m/s$

$\frac{dv}{dt}=5dv=5dt{\int }_0^{v}dv=5{\int }_0^{t}dtv=5t1=5t\Rightarrow t=\frac{1}{5}=0.25$