A 1100 kg automobile is at rest at atraffic signal. At the instant the light tur

Question

A 1100 kg automobile is at rest at atraffic signal. At the instant the light turns green, theautomobile starts to move with a constant acceleration of6.0 m/s2. At the same instant a3200 kg truck, traveling at a constantspeed of 9.0 m/s, overtakes and passes theautomobile. (a) How far is the center of mass of theautomobile truck system from the traffic light at t = 3.0s?
1 m

(b) What is the speed of the center of mass of the automobile-trucksystem then?
2 m/s (a) How far is the center of mass of theautomobile truck system from the traffic light at t = 3.0s?
1 m

(b) What is the speed of the center of mass of the automobile-trucksystem then?
2 m/s

Explanation / Answer

At t = 3.0 s, the position of theautomobile is x1 = ½ at2 =27m

and its velocity is v1 =at = 18.0 m/s

The truck moves at constantvelocity v2. At t = 3.0 s is position is x2 =v2t = 27 m

and its speed is 9.0 m/s

(a) The position of the center ofmass is

xCofM =(m1x1 +m2x2)/(m1 + m2) =(1100*27 + 3200*27)/(1100 + 3200) = 27m

(b) The velocity of the center ofmass is

vCofM =(m1v1 +m2v2)/(m1 + m2) =(1100*18.0 + 3200*9.0)/(1100 + 3200) = 11.30 m/s

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