91Ó°ÊÓ

The basic difference in speed and velocity is that speed is a scalar quantity, and velocity is a vector quantity. Speed is the change in position in unit time, and velocity is the change in displacement in unit time.

Given data.

For the first part, the horse went away at a distance of 38 m in 9.0 s.

For the second part, it comes back at halfway within 1.8 s.

Assumptions.

Let the initial position of the horse be at 0 m. Then, after the first part of the motion, the position of the horse is 38 m, and the final position is 19 m.

Now, you know that

$\begin{array}{c}\mathrm{Average}\mathrm{speed}=\frac{\mathrm{Total}\mathrm{distance}}{\mathrm{Total}\mathrm{time}}\\ \mathrm{Average}\mathrm{velocity}=\frac{\mathrm{Total}\mathrm{displacement}}{\mathrm{Total}\mathrm{time}}\end{array}$

Now, the total distance is the sum of the distances in the first and second parts.

$\begin{array}{c}\mathrm{d}=\mathrm{distance}\mathrm{for}\mathrm{first}\mathrm{part}+\mathrm{distance}\mathrm{for}\mathrm{second}\mathrm{part}\\ =\left|38\mathrm{m}-0\mathrm{m}\right|+\left|19\mathrm{m}-38\mathrm{m}\right|\\ =38\mathrm{m}+19\mathrm{m}\\ =57\mathrm{m}\end{array}$

The total displacement is the straight line distance between the initial and final positions. So,

$\begin{array}{c}\mathrm{d}\text{'}=\mathrm{straight}\mathrm{line}\mathrm{distance}\mathrm{between}\mathrm{the}\mathrm{final}\mathrm{and}\mathrm{initial}\mathrm{position}\\ =\mathrm{position}\mathrm{ofthefinalpoint}-\mathrm{positionoftheinitialpoint}\\ =19\mathrm{m}-0\mathrm{m}\\ =19\mathrm{m}\end{array}$

The total time required for the motion of the horse is

$\begin{array}{c}\mathrm{Δ}t=\left(9.0\mathrm{s}+1.8\mathrm{s}\right)\\ =10.8\mathrm{s}\end{array}$

Therefore,

$\begin{array}{c}\mathrm{average}\mathrm{speed}=\frac{57\mathrm{m}}{10.8\mathrm{s}}\\ =5.28\frac{\mathrm{m}}{\mathrm{s}}\\ \mathrm{average}\mathrm{velocity}=\frac{19\mathrm{m}}{10.8\mathrm{s}}\\ =1.76\frac{\mathrm{m}}{\mathrm{s}}\end{array}$

(a) Hence, the average speed of the horse is $5.28\frac{\mathrm{m}}{\mathrm{s}}$.

(b) Hence, the average velocity of the horse is $1.76\frac{\mathrm{m}}{\mathrm{s}}$.