The displacement of a particle is metres

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

Problem

The displacement of a particle is s(t)=t3−6t2+9ts(t)=t^{3}-6t^{2}+9t metres, where tt is in seconds. (i) Find the average velocity on the interval [1 s, 3 s][1\,\text{s},\,3\,\text{s}]. (ii) Find the instantaneous velocity at t=3t=3 s. Select the correct ordered pair (average velocity, instantaneous velocity)(\text{average velocity},\ \text{instantaneous velocity}). (a) (2 m/s, 0 m/s)(2\,\text{m/s},\ 0\,\text{m/s}) (b) (−2 m/s, 0 m/s)(-2\,\text{m/s},\ 0\,\text{m/s}) (c) (−4 m/s, 0 m/s)(-4\,\text{m/s},\ 0\,\text{m/s}) (d) (−2 m/s, −2 m/s)(-2\,\text{m/s},\ -2\,\text{m/s})

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