Mathematics

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. (a) Obtain general expressions for the velocity

v(t)

and acceleration

a(t)

in terms of

k

and

m

. b. (b) Taking

k=0.2

and

m=3

, find the smallest positive time

t

at which the velocity is zero. c. (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.

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