QUIZ 1

1. A student throws a set of key vertically upward to her classmate in a window 4.00m above. The keys are caught 1.50s later by the classmate's outstretched hand. (a) With what initial velocity were the keys thrown? (b) What was the velocity of the keys just before they were caught?

Solution.

(a) Taking y0 = 0 (at the position of the thrower) and given that y = 4.00m at t =1.50s, we find (with a = -9.80m/s2)

                              y = v0t+ 1/2at2   or v = (y - 1/2at2)/t

                             v0 = [4.00m - 1/2(-9.80m/s2)(1.50s)2]/(1.50s) = 10.0m/s

(b) The velocity at any time t > 0 is given by v = v0 + at.

      Therefore , at t = 1.50s,

                             v = 10.0m/s - (9.80m/s)(1.50s) = -4.68m/s

 

2. An object is moving from rest with a varying acceleration a = (5m/s3)t, where t is in seconds. Find (a)  the instantaneous velocity, and the position of the object at t = 4.0s. Assume that the object starts from x0 = 0 .

Solution.

 (a) At any time t > 0, the instantaneous velocity is given by

                              v =  ò adt =  ò (5m/s3)tdt = (5/2m/s3)t2 + C

      At t = 0, v0 = 0, we have C = 0.

      At t = 4.0s,    v = (5/2m/s3)(4.0s)2 = 40.0m/s.

 (b) At any time t > 0, the position of the object is given by

                              x =   vdt =   (5/2m/s3)t2dt = (5/2m/s3)t3/3 + C1.

      At t = 0, x0 = 0, we have C1 = 0

      At t = 4.0s,      x = (5/2m/s3)(4.0s)3/3 = 53.3m.