A particle moves along a straight line so that its position at time seconds is given…

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

Problem

A particle moves along a straight line so that its position at time

t

seconds is given by the polynomial function

s(t)=3t^{5}-10t^{3}+4

(position is measured in meters). (a) Calculate the instantaneous velocity

v(t)

of the particle as a function of

t

. Express your answer in meters per second. (b) Evaluate

v(2)

and interpret its physical meaning in the context of the motion. (c) Determine the equation of the line tangent to the graph of

y=s(t)

at the point corresponding to

t=2

. Express your answer in point-slope form.