Question

a point moves along a circle of radius 20 cm with constant tangential acceleration of 5cm s'2.the time after which the normal acceleration of the point will be equal to tangential acceleration​

Answer 1

according to given question

tangential acceleration and normal (centripetal accleration) acceleration are equal.

Answer 2

At t = 2 seconds, the time after which the normal acceleration of the point will be equal to tangential acceleration​

Explanation:

Given that,

Radius of the circular path, r = 20 cm

Tangential acceleration, $a_t=5\ cm/s^2$

Tangential acceleration is :

$a_t=\dfrac{v^2}{r}\\\\v=\sqrt{a_t\times r}\\\\v=\sqrt{5\times 20}\\\\v=10\ cm/s$

We need to find the time after which the normal acceleration of the point will be equal to tangential acceleration​ such that :

$a_t=a_c$

Here, u = 0

$v=u+at\\\\v=at\\\\t=\dfrac{v}{a}\\\\t=\dfrac{10}{5}\\\\t=2\ s$

So, at t = 2 seconds, the time after which the normal acceleration of the point will be equal to tangential acceleration​

Learn more,

Acceleration