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Centripetal Acceleration

A particle is...

Question

A particle is moving on a circular path of radius R. Its centripetal acceleration vs time graph is given, then corresponding tangential acceleration vs time graph is best represented by

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Solution

The correct option is D
$a_{c} = k t$ & $a_{c} = \frac{v^{2}}{R} \Rightarrow v^{2} = k R t \Rightarrow 2 v \frac{d v}{d t} = k R \Rightarrow a_{t} = \frac{k R}{2 v} = \frac{k R}{2 \sqrt{k R t}}$

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Table-1	Table-2
(A) Magnitude of tangential acceleration of particle	(P) decreases with time
(B) Magnitude of centripetal acceleration of particle	(Q) increases with time
(C) Magnitude of angular speed of particle with respect to centre of circle	(R) remains constant
(D) Angle between the total acceleration and centripetal acceleration of particle	(S) depends on the value of radius

12 m

S = 2 t^{3}

t = 2 s

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