Question

16. A particle moves in a circle of radius 30 cm. Its
linear speed is given by v = 2t where t in second
and v in m/s. Find out its radial and tangential
acceleration at t = 3 sec respectively,​

Answer 1

tangential acceleration= 2m/s²

radial acceleration = 120 m/s²

Explanation:

Tangential acceleration = d(v)/d(t) = 2

Radial acceleration = v²/r

Answer 2

Answer:

The radial and tangential acceleration of the particle are $120m/s^2$ and $2m/s^2$ respectively.

Explanation:

Given that,

A particle moves in a circle of radius 30cm.Its linear speed is given by $v=2t$

We are required to find its radial and tangential acceleration at time $t=3sec$.

The radial acceleration is given by the relation

$a_{R}=\frac{v^2}{R}=\frac{(2t)^{2}}{R} \\(a_{R})_{t=3}=\frac{4(3^2)}{0.3} =120m/s^2$

The tangential acceleration is given by the relation

$a_{T}=\frac{dv}{dt}=\frac{d}{dt}(2t)=2m/s^{2}$

Therefore,

The radial and tangential acceleration of the particle are $120m/s^2$ and $2m/s^2$ respectively.

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