Do not forget your LABELS. Two cars, A and B, start at the same position with th

Question

Do not forget your LABELS. Two cars, A and B, start at the same position with the same speeds and moving in the same direction. Car A stays at that same speed, but car B decelerates with constant acceleration, -a (a is a positive real number.) a) [4 pts] Draw complete motion maps for A and B. b) [2 pts] At the instant that B reaches a speed of zero, what is the ratio of the distances travelled by A and B? c) [2 pts] Draw a reasonably accurate graph of x vs t for both cars (one graph containing both curves), d) [2 pts] You should find that the ratio is a simple number, independent of any of the given quantities. Give a clear argument that explains this independence.

Explanation / Answer

The motion picture are not getting loaded! Draw v vs t, a vs t and x vs t curves.
b) Equation of B is v = u0 - at. When v = 0, t = u0/a. Distamce travelled by B is xb = u0t - 1/2 at2,

xb = (u02)/a - u02/2a = u02/2a.

At same time t = u0/a, xa = u0t = u02/a.

Ratio of xa:xb = 2:1

d) As both are in same direction and with same initial conditions, the ratio is independent.

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