Question

# The graph shown illustrates velocity versus time for two cars A and B constrained to move in a straight line. Both cars were at the same position at t=0 s. Consider the following statements. (1) Car A is travelling west, and Car B is travelling east. (2) Car A overtakes Car B at t=5 s (3) Car A overtakes Car B at t=10 s . Which of the following is correct?

A
Only statement 1 is true
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B
Only statement 2 is true
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C
Only statement 3 is true
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D
Only statement 1 and 2 are true
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Solution

## The correct option is D Only statement 3 is trueSince for both velocities are positive, both are moving in the same direction. The distance travelled is the magnitude of area under v−t curve. At t=10 sec Area under v−t curve for car A, AA=12×10×10=50 units. Area under v−t curve for car B, AB=12×(7+3)×10=50 units. Since area for both cars is 50 units, therefore car A will overtake car B in 10 sec

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