Question

Mr. Mangan runs 50 m north in 5 seconds, 50 m east in 7 seconds, and50 m south in 3 seconds. What is his average speed? What is hisaverage velocity?

Answer 1

Mr. Mangan goes first in the north a distance

$d_1=50\text{ m}$

at time,

$t_1=5\text{ s}$

then towards east ,

$d_2=50\text{ m}$

in time,

$t_2=7\text{ s}$

after that he goes towards south a distance,

$d_3=50\text{ m}$

in time,

$t_3=3\text{ s}$

the average speed is,

$\begin{gathered} s=\frac{total\text{ distance }}{\text{total time}} \\ =\frac{50+50+50}{5+7+3} \\ =10\text{ m/s} \end{gathered}$

The average velocity is,

$v=\frac{displacement}{\text{total time}}$

Here the displacement is,

$d^{\prime}=50\text{ m}$

The average speed is,

$\begin{gathered} v=\frac{50}{5+7+3} \\ =3.33\text{ m/s} \end{gathered}$

The average velocity is,

$v=3.33\text{ m/s along east}$