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A particle moves in a circle of radius 20 cm. Its linear speed is given by v=2t, where t is in second and v is in m/s. Find the radial and tangential acceleration at t= 3s .

A particle moves in a circle of radius 20 cm. Its linear speed is given by v=2t, where t is in second and v is in m/s. Find the radial and tangential acceleration at t= 3s .

Grade:12th pass

2 Answers

Apoorva Arora IIT Roorkee
askIITians Faculty 181 Points
9 years ago
The linear speed at t= 3 s is

v= 2t = 6 m/s.

The radial acceleration at t= 3 s is

a_{r} = v^{2}/r = \frac{36 m^{2}/s^{2}}{0.20 m} = 180 m/s^{2}.

The tangential acceleration is

a_{t} = \frac{\mathrm{d} v}{\mathrm{d} t} = \frac{\mathrm{d} (2t)}{\mathrm{d} t} = 2 m/s^{2}.
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the attached solution to your question.
at time, t = 3s
Linear speed, v = 2t = 2 x 3 = 6m/s
radial acceleration, ar = v2/r = 62/0.2 = 36/0.2 = 180m/s2
Tangential acceleration, at = dv/dt = d(2t)/dt = 2m/s2
Hope it helps.
Thanks and regards,
Kushagra

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