Question

A particle moves in a circle of radius 1 cm at speed given by v = 2t where v is in cm/s 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

V = 2t, r = 1 cm

(a) Radial acceleration at t = 1 sec

$\alpha =\left(\frac{v^2}{r}\right)=\frac{(2{)}^2}{1}=4cm/se{c}^2$

(b) Tangential acceleration at t = 1 sec

$\alpha =\frac{dv}{dt}=\frac{d}{dt}\left(2t\right)=2cm/se{c}^2$

(c) Magnitude of acceleration at t = 1 sec

$\alpha =\sqrt{4^2+2^2}=\sqrt{20}cm/se{c}^2$