A particle moves along a horizontal line so that its position

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

Problem

A particle moves along a horizontal line so that its position, in meters, at time

t

seconds is given by

s(t)=20t-5t^{2}

for

0\le t\le 6

. (a) Derive an expression for the particle’s instantaneous velocity

v(t)

. (b) Determine the time or times in the interval

0\le t\le 6

at which the particle is at rest. (c) Determine the time at which the particle is farthest to the right of the origin on the interval

0\le t\le 6

, and state that maximum distance. Justify that your result gives a global maximum on the interval. (d) On what sub-intervals of

0\le t\le 6

is the particle moving to the left? Give your answer in interval notation and justify algebraically.