Question

Wheel A of radius ra = 13.9 cm is coupled by belt B to wheel C of radius rc = 34.3 cm. Wheel A increases its angular speed from rest at time t = 0 s at a uniform rate of 5.7 rad/s2. At what time will wheel C reach a rotational speed of 168.2 rev/min, assuming the belt does not slip?

so for c: v = w*r = 168.2*0.343m =57.6926
and therefore for a: w = v/r = 57.6926/0.139m = 415.055
is that correct?

and for the acceleration:
for a: a= 5.7*0.139 = 0.7923
and for c: 0.7923/0.343 = 2.3099

but how do I get time ??

Answer 1

Your calculations look OK except:
(1) w has to be in radians per second, not rpm.

(2) You need to include dimensions with the numbers.

For example v is in m/s and a is in m/s^2. For the time required, divide the final angular velocity of C by its angular acceleration rate, 5.7 rad/s^2. .