A1100 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 2000 kg truck, traveling at a constant speed of 7.0 m/s, overtakes and passes the automobile. a)how far is the com of the automobile-truck system from the traffic light at t=3.0 s? b)what is the speed of the com then?

a ) 21 m b) 7 m/s

Explanation:

For this case, we can consider for our reference system, that point zero (this is, at the rest of the traffic signal) is when X₀ = 0, and direction of movement is from left to right (positive sign)

For the car:  

a= acceleration is constant = 5 m/s² m1 , mass = 1100 Kg , V = not constant

This is an uniformly accelerated rectilinear movement, and applicable formulas are:

V = V₀ + at , X = X₀ + V₀t + 1/2at²

For the truck:

V = speed is constant = 7 m/s , mass = 2000 Kg, a = 0

This is an uniform rectilinear movement, and the applicable formula is:

X = X₀ + Vt

a)At t = 3.0 sec, we can use the formula for the track, considering that X₀ = 0 (when it pass the rest of the traffic signal)

X = 0 + (7 m/s)x(3 s) = 21 m  

So, at 3 sec, truck will be at 21 m from the rest of traffic light and, as truck has a constant speed; at that exact second; truck and car will be together as a com, so both will be 21 m away from point zero

b)At the exact time (3 sec, or in distance words, 21 m) car and truck will be together as a com, so they will both have the exact speed, hence, speed of car at that point will be 7 m/s

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