A suitcase is placed on a horizontal conveyor belt. The coefficient of static friction between the suitcase and the belt is 0.3 . If the belt starts from rest and accelerates uniformly, what is the minimum time it can take to reach a speed of 12 m/s without the suitcase sliding on the belt? (Take g = 10 m/s ^2 )

Step-by-step solution

For the suitcase not to slide on the conveyor belt, the maximum acceleration of the belt cannot exceed the maximum acceleration provided by static friction. The maximum static friction force is given by: f_ s, max = _s m g The maximum acceleration a_ max of the suitcase without sliding is: a_ max = f_ s, max m = _s g Substituting the given values _s = 0.3 and g = 10 m/s ^2 : a_ max = 0.3 10 = 3 m/s ^2 The belt starts from rest ( u = 0 ) and accelerates uniformly to a final speed v = 12 m/s . Using the first equatio