Question

A particle moves in a circle of radius 1.0 cm at a speed given by v=2.0t where v is in cm/s and and t in seconds.
(a) Find the radial acceleration of the particle at t=1 s. (b) Find the tangential acceleration at t=1 s (c) Find the magnitude of the acceleration at t = 1 s.

Answer 1

Given conditions ⇒

v = 2t.

(a). Radial Acceleration in magnitude will always be constant.

∴ It will not depends upon the Instantaneous velocity and will be constant throughout the motion.

∴ Velocity =  2t = 2(1) = 2 cm/s.

∴ Radial Acceleration = v²/r = 2²/1 = 4 cm/s²

(b). Tangential acceleration,

v = 2t

Differentiating both sides w.r.t time,

a = 2 cm/s²

∴ tangential acceleration is 2 cm/s².

(c).  Now Magnitude of the acceleration = $\sqrt{(4)^2 + (2)^2}$

= $\sqrt{20}$ cm/s².

Hope it helps.

Answer 2

Explanation:

(a) 4

(b) 2

(c) 2√5

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