Mathematics

Problem

The position of a particle moving along the

x

-axis is described by

x(t)=4t^{3}-18t^{2}+24t

, where

x

is in metres and

t

in seconds. a. (a) Obtain an expression for the instantaneous velocity

v(t)

. b. (b) Find the time interval(s) during which the particle moves in the positive

x

-direction. c. (c) Write an expression for the instantaneous speed

s(t)

as a function of time. d. (d) Calculate the total distance travelled by the particle between

t=0\,\text{s}

and

t=4\,\text{s}

. Show all working clearly.