Mathematics

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}

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

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

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