A particle moves along a straight track so that its acceleration at time seconds is…

MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

A particle moves along a straight track so that its acceleration at time

t

seconds is given by

a(t)=6t-4

(in m/s

^{2}

). At

t=0

the particle is located 2 m to the right of the origin and is moving to the left with velocity 3 m/s. (a) Determine the velocity function

v(t)

for

t\ge 0

. (b) Determine the position function

s(t)

for

t\ge 0

measured from the origin. (c) Find all times in the interval

0\le t\le4

at which the particle is momentarily at rest, and classify each as a relative maximum, minimum, or neither for

s(t)

. (d) Compute the total distance traveled by the particle during the first 4 seconds.