The distance of a particle moving on a circle

Asked by admin @ 23/08/2021 in Physics viewed by 300 People

the distance of a particle moving on a circle of radius 12 m measured from a fixed point on the circle and measured along the circle is given by s = 2t3 (in metres). find the ratio of its tangential to centripetal acceleration at t = 2s.

Answered by admin @ 23/08/2021

Given,

S = 2t³

Differentiating both the sides with respect to the time.

dS/dt = d(2t³)/dt

⇒ Velocity = 2 × 3 × t²

⇒ Velocity = 6t².

Centripetal Acceleration = V²/R = (6t²)²/12 = 36t⁴/12 = 3t⁴ = 48 m/s².

Now, Tangential Acceleration = d|v|/dt = d|6t²|/dt = 2 × 6 × t = 12t = 12 × 2 = 24 m/s².

∴ Ratio of Tangential and Centripetal acceleration = 12t/3t⁴

= 24/48

= 1/2

= 1 : 2

Hope it helps.

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