Question

What is the displacement of the cross- country team if they begin at the school, run $10miles$ and finish back at the school?

Answer 1

HintWe will take into account the initial and final position of the team. Then we will find the displacement as the difference in initial and final position.
Formulae Used: \[s = \Delta x\]
Where, \[s\] is the displacement, \[\Delta x\] is the change in position.

Step By Step Solution
Here,
Given that the team starts at the school.
That means the initial position of the team, \[{x_i}\] is say\[{x_1}\].
Again,
They run a $10miles$.
Thus, their next position will be, \[{x_2} = {x_1} + 10\]
Then,
Finally they finish at school.
Thus,
Final position of the team,\[\;{x_f}\] is \[{x_1}\].
Hence,
We can say,
\[s = \Delta x = {x_1} - {x_1} = 0{\text{ }}units\]

Additional InformationUnlike distance, displacement only attains the value of the change in the position of the body whereas distance tells us about the actual path length a body covers. Since, displacement is the change in position, hence, it can have a positive, negative or zero value. Whereas if a body is moving, then its distance cannot be negative or zero at any situation.
Also, the change in distance is referred to as speed which in turn cannot be negative or zero for a moving body but the change in displacement which is referred to as velocity could be negative, positive or zero.

Note: From the evaluated answer, we can say that when a body finishes its journey at the same point it started on, the displacement turns out to be zero.
We have written the answer to be $0units$, the units part can take any unit of length may it be $m$ or $cm$ but whatever the unit may be, the net value is zero in and all for all.