A 1100 kg automobile is at rest at a traffic signal At the i

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 5.0 m/s2. At the same instant a 2100 kg truck, traveling at a constant speed of 6.0 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 = 4.4 s? (b) What is the speed of the center of mass of the automobile-truck system then?

Solution

We use the constant-acceleration equations with the origin at the traffic light

At t = 4.4.0 s, the location of the automobile (of mass m1) is x1=1/2*a*t^2=0.5*5*4.4^2=48.4m

while that of the truck (of mass m2) is x2 = v*t = (6.0 m/s)(4.4s) = 26.4 m

The speed of the automobile then is : v1=a*t=5*4.4 =22m/s,

while the speed of the truck remains v2 = 8.0 m/s.

(a) The location of their center of mass is

xcm=(m1*x1+m2*x2)/(m1+m2) =(1100*48.4+2100*26.4)/(1100+2100) =33.9625m

b) The speed of the center of mass is v_com =(m1*v1+m2*v2)(m1+m2) =(1100*22+2100*8)/3200=12.8125m/s