A particle moving along a coordinate axis has acceleration (in meters per second…

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

Problem

A particle moving along a coordinate axis has acceleration (in meters per second squared) given by

a(t)=\sin t+2

for

0\le t\le 2\pi

. At time

t=0

the particle’s velocity is

1\text{ m/s}

and its position is

3\text{ m}

. (a) Find

v(t)

given

a(t)

and the initial condition. (b) Determine

s(t)

given the initial position. (c) Compute the average velocity on

[0,2\pi]

. (d) Decide whether the average velocity is zero with justification. (e) Compare total distance traveled with displacement and justify.