Question

A particle moves in a circle of radius 20 cm. It’s linear speed is given by v = 2t where t is in second and v in metre/s. Find the radial and tangential acceleration at t = 3s.

Answer 1

at t =3s

linear speed = 6m/s

its angular velocity = 6/0.2= 30 rad/s

radial acceleration = 6×6/0.2 = 180 rad/s^2

tangential acceleration = angular acceleration ×radius

= 6×6= 36m/s^2

Answer 2

Solution :

Given,

v = 2t

r = 20 cm

t = 3 s

By using the formula of radial acceleration.

Radial acceleration = v^2 / r

Radical acceleration = v^2 / r

Radical acceleration = (2t)^2 / 0.2

Radical acceleration = 4t^2 / 0.2

Radical acceleration = 4 × t^2 / 0.2

Radical acceleration = 4 × 3^2 / 0.2

Radical acceleration = 4 × 9 / 0.2

Radical acceleration = 180 m/s^2.

.°. Radical acceleration = 180 m/s^2.

Now,

By using the formula of tangential acceleration.

Tangential acceleration = dv / dt

Tangential acceleration = dv / dt

Tangential acceleration = d(2t) / dt

Tangential acceleration = 2 m/s^2

.°. Tangential acceleration = 2 m/s^2