A particle moves in a circle of radius 1.0 cm at a speed given by u = 2.0 t where u 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.
(b) 2.0 cm/s2
(c)
Radius, r = 1.0 cm
(a.) t = 1s
Velocity of the particle, u = 2.0 t = 2.0×1 = 2.0 cms-1
Radial acceleration of the particle = v2/r= (2.0)2/10 = 4.0 cm/s2
(b.) It is given that v=2t
Differentiating both sides with respect to time,
⇒ 
⇒ a=2 cms-2
⇒ Tangential acceleration, a = 2 cm/s2
(c.) Magnitude of acceleration = 
= 
= 
cm/s2
1