Two cars, A and B, start side by side and accelerate from rest. The figure shows
ID: 2883547 • Letter: T
Question
Two cars, A and B, start side by side and accelerate from rest. The figure shows the graphs of their velocity functions and a = 4. (a) Which car is ahead after four minutes? car A car B Explain. The area under curve A is greater than the area under curve B. The area under curve B is greater than the area under curve A. (b) What is the meaning of the area of the shaded region? It is how much faster A is traveling than B after 4 minutes. It is how much faster B is traveling than A after 4 minutes. It is the distance by which A is ahead of B after 4 minutes. It is the distance by which B is ahead of A after 4 minutes. (c) Which car is ahead after eight minutes? car A car B Explain. The area under curve A is greater than the area under curve B. The area under curve B is greater than the area under curve A. (d) Estimate the time t at which the cars are again side by side. t = minExplanation / Answer
Answer a)
Car A is ahead of Car B
Reason:- The area under v-t graph gives us the displacement of the moving object.
The area covered by Curve A from t=0 to t=4 is larger than area covered by Curve B from t=0 to t=4.
Hence Car A is ahead of Car B
Answer b) The shaded region represents the difference of area covered by them which is difference in the displacement of the both cars from t=0 to t=4. Hence It is the distance by which Car A is ahead of Car B after 4 mins.
Answer c) After 8 minutes Car B is ahead . because after 8 minutes the area covered by Curve B after 8 minutes is larger than area covered by Curve A.
Hence Car B is ahead of Car A
Answer d) at t=8 , because from t=0 to t=8 , the area covered by both the curves are almost equal.
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