Which of the following expressions gives the average speed of a particle whose…

MATHEMATICS · Single correct · AP · Calculus BC · Applications of Integration · Applications of Integration

Problem

Which of the following expressions gives the average speed of a particle whose position vector is

\mathbf r(t)

for

a\le t\le b

? (a)

\displaystyle\frac{|\mathbf r(b)-\mathbf r(a)|}{b-a}

(b)

\displaystyle\frac{1}{b-a}\int_a^b |\mathbf r'(t)|\,dt

(c)

\displaystyle\left|\frac{1}{b-a}\int_a^b \mathbf r'(t)\,dt\right|

(d)

\displaystyle\sqrt{\frac{1}{b-a}\int_a^b |\mathbf r'(t)|^2\,dt}