A particle moves along a straight line with position meters for seconds

MATHEMATICS · Single correct · A Level · Mathematics · Kinematics · Kinematics

Problem

A particle moves along a straight line with position s(t)=3t3−15t2+18ts(t)=3t^{3}-15t^{2}+18t meters for 0≤t≤40\le t\le 4 seconds. Which statement correctly compares the average velocity over the interval 0≤t≤40\le t\le 4 with the instantaneous velocity at t=2t=2 seconds? (a) The average velocity is 6 m/s6\,\text{m/s}, and the instantaneous velocity at t=2t=2 is 0 m/s0\,\text{m/s}; they differ in both magnitude and direction. (b) The average velocity is 12 m/s12\,\text{m/s}, and the instantaneous velocity at t=2t=2 is −6 m/s-6\,\text{m/s}; they differ in both magnitude and direction. (c) The average velocity is 6 m/s6\,\text{m/s}, and the instantaneous velocity at t=2t=2 is −6 m/s-6\,\text{m/s}; they have equal magnitude but opposite directions. (d) The average velocity is 6 m/s6\,\text{m/s}, which equals the instantaneous velocity at t=2t=2 in both magnitude and direction.

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