Two cars, A and B, start side by side and accelerate from rest. The figure shows
ID: 2887179 • 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 = 5.
(a) Which car is ahead after five minutes?
car Acar 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 5 minutes.It is how much faster B is traveling than A after 5 minutes. It is the distance by which A is ahead of B after 5 minutes.It is the distance by which B is ahead of A after 5 minutes.
(c) Which car is ahead after ten minutes?
car Acar 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 = min
Explanation / Answer
(a) Car A is ahead after 5 minutes, because its velocity curve is always above the velocity curve of car B during the first 5 minutes.
Explain.
The area under curve A is greater than the area under curve B.
(b) It is the distance by which A is ahead of B after 5 minutes.
Since the curve of A is above Curve of Car B, so the area denotes the extra distance which car A tracels. Recall that area under velcity time curve, gives the value of distance covered.
(c) car A is ahead after ten minutes.
Explain.
The area under curve A is greater than the area under curve B.
From the sketch, it is clear that the area between Curve A and B from t=0 to 5 min is more than the area between Curve B and A from t=5 to 10. So Car is is till ahead.
(d) Since Car B is moving faster than Car A after 5 minutes, so an approximate value by which the two cars will again be side by side is when the area between Curve B and A from t=5 onwards, equals the area between Curve A and B from t=0 to 5 min. An approximate value of this time is t=12 min.
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