A particle moves along a straight line with acceleration given by a(t)=3t^ 2 -4t+1 (…

MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

A particle moves along a straight line with acceleration given by

a(t)=3t^{2}-4t+1\quad(\text{m/s}^2)

for

0\le t\le 5

seconds. Its velocity and position satisfy

v(0)=2\text{ m/s}

and

s(0)=7\text{ m}

. (a) Derive an expression for the velocity

v(t)

of the particle for

0\le t\le 5

. (b) Derive an expression for the position

s(t)

of the particle for

0\le t\le 5

. (c) Determine the particle’s average velocity on the time interval

0\le t\le5

. Show all work, including appropriate units. (d) Compute the total distance traveled by the particle on

0\le t\le5

. Justify any sign changes you consider.