Question

A 1000 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 3.2 m/s2. At the same instant a 2250 kg truck, traveling at a constant speed of 8.8 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 = 2.1 s? (b) What is the speed of the center of mass of the automobile-truck system then?

Answer 1

let m1 = 1000 kg

position of m1 after t = 2.1 s,

x1 = vox*t + (1/2)*a*t^2

= 0 + (1/2)*3.2*2.1^2

= 7.06 m

m2 = 2250 kg

x2 = v2*t

= 8.8*2.1

= 18.48 m

the center of mass of the automobile-truck system from the traffic light at t = 2.1 s,

Xcm = (m1*x1 + m2*x2)/(m1 + m2)

= (1000*7.06 + 2250*18.48)/(1000 + 2250)

= 15.0 m <<<<<<<------Answer

b) v1 = vo + a*t

= 0 + 3.2*2.1

= 6.72 m/s

so,

vcm = (m1*v1 + m2*v2)/(m1 + m2)

= (1000*6.72 + 2250*8.8)/(1000 + 2250)

= 8.16 m/s <<<<<<<------Answer