A particle moves along a straight line so that its displacement from the origin at…

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A particle moves along a straight line so that its displacement from the origin at time

t

seconds is

s(t)=5t^{2}-2t+3

metres. (i) Calculate the instantaneous velocity of the particle at

t=4\text{ s}

. (ii) Find the equation of the tangent to the graph of

s

versus

t

at the point corresponding to

t=4\text{ s}

. Present your answer in the form

s=mt+c

, where

m

and

c

are constants.