The position of a particle is x=t³-6t²-15t+40, with x in m and t in s. Which graph does not represent the motion of the particle?
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Question

The position of a particle is x=t³-6t²-15t+40, with x in m and t in s. Which graph does not represent the motion of the particle?

G1 Physics · Accepted Answer

x=t³-6t²-15t+40. Then v=3(t-5)(t+1), so for t≥0 velocity is negative until 5 s and positive after 5 s. Also a=6(t-2), changing sign at 2 s. Therefore x(t) decreases, changes concavity at 2 s, has a minimum at 5 s and then rises. The graph inconsistent with these features is Image 4. Hence option D.