The displacement (in metres) of a point mass moving along a line is described by…

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

Problem

The displacement

s(t)

(in metres) of a point mass moving along a line is described by

s(t)=e^{kt}\cos(mt),

where

k>0

and

m>0

are constants and

t

is measured in seconds. (a) Obtain general expressions for the velocity

v(t)

and acceleration

a(t)

in terms of

k

and

m

. (b) Taking

k=0.2

and

m=3

, find the smallest positive time

t

at which the velocity is zero. (c) Using the value of

t

obtained in part (b), calculate the corresponding acceleration and state, with reason, whether the speed of the particle is increasing or decreasing at that instant.

Related theory

Differentiation Rules
Motion
Rates of change
Rate of change of quantities

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