Question

A 1100 kg automobile is at rest at a traffic signal. At the instant the light turns green, the automobile starts to move with a constant acceleration of 3.0 m/s2. At the same instant a 2800 kg truck, traveling at a constant speed of 8.0 m/s, overtakes and passes the automobile. (a) How far is the center of mass of the automobile–truck system from the traffic light at t= 3.0s? (b) What is the speed of the center of mass of the automobile-truck system then?

Answer 1

First write the location of the auto and of the truck as a function of time after the light turns green (t). Call these locations X1 and X2.

X1 = 1.5 t^2 (the auto)
X2 = 8.0 t (the truck)

The center of mass location is
X3 = (1100 X1 + 2800 X2)/3900.

The speed of the CM is dX3/dt
V3 = [1100*3t + 2800*8]/3900

Finish the calculation