5. The position of two particles, A and B, are given in the x versus t graph. As
ID: 1708683 • Letter: 5
Question
5. The position of two particles, A and B, are given in the x versus t graph. Assume the particles move along tracks that are placed side-by-side.
(a) At t = 0 s particle B (indicated by dashed line) is 5 m ahead of A. During the time interval shown, is there another instant when this is true? If your answer is yes, state the approximate time when this occurs. If your answer is no, state that explicitly. In either case, explain your reasoning.
(b) Do the particles simultaneously have the same velocity (magnitude and direction)? If so, at what time does this occur? Explain.
Explanation / Answer
(a) there are two points on the line of B , (0,5) and (30,10) , so we can write down this equation x(t) of B = t/6 + 5 and also the equation x(t) of A = -0.0178(t-26.5)^2 + 12.5 x(t)_B - x(t)_A = 5 = (t/6 + 5) - [-0.0178(t-26.5)^2 + 12.5] = 0.0178(t-26.5)^2 + t/6 - 7.5 t ? 0 or 43.64(s) ? B is 5m ahead of A when t equals about 43.64 second! (b) ? x(t)_B = t/6 + 5 ?v(t)_B = 1/6 ( by derivativing) ? x(t)_A ? 0.0178(t-26.5)^2 + t/6 - 7.5 ? V(t)_A ? 0.0356(t-26.5) if v(t)_A = v(t)_B , then 1/6 = 0.0356*(t-26.5) , t = 31.18(s) so the velocity of B equals that of A when t is 31.18 second!
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