A particle moves along a straight line so that its position (in meters) at time…

MATHEMATICS · Multi-part · A Level · Mathematics · Kinematics · Kinematics

Problem

A particle moves along a straight line so that its position (in meters) at time

t

seconds is given by

s(t)=3t^3-18t^2+24t-5

for

0\le t\le 6

. (a) Calculate

s(0)

and

s(6)

, including units. (b) Determine the particle’s average velocity, in meters per second, over the interval

0\le t\le 6

. Show all work that leads to your result. (c) Compute the instantaneous velocity

v(t)

of the particle, and find all times

t

in the open interval

(0,6)

at which

v(t)

equals the average velocity found in part (b). Justify your answer(s). (d) Describe the physical significance of the value(s) of

t

obtained in part (c) in the context of the particle’s motion.