A particle moves along a straight line for seconds

MATHEMATICS · Multi-part · A Level · Mathematics · Kinematics · Kinematics

Problem

A particle moves along a straight line for

t \ge 0

seconds. Its acceleration (in m/s

^2

) is given by

a(t)=s''(t)=6t-4.

t=1

, the velocity is

3\text{ m/s}

, and at

t=0

the particle is located

2\text{ m}

to the left of the origin. (a) Determine the velocity function

s'(t)

for

t \ge 0

. State its units. (b) Determine the position function

s(t)

for

t \ge 0

. State its units. (c) Calculate the particle’s total displacement on the time interval

0 \le t \le 2

. Interpret your result in the context of the motion.