Question

Three different people move on the same track, which is $400\,{\text{m}}\ ]in circumference. The track has two straight portions that are over \[100\,{\text{m}}$ in length and the two curves are each under $100\,{\text{m}}$ in length.Person ${\text{1}}$ walks straight northward on the track for $100\,{\text{metres}}$, starting at point S and finishing at point F ${\text{50 seconds}}$ later.Person ${\text{2}}$ starts out southward from point S and runs part way around the track, finishing at the same F as person ${\text{1}}$ in ${\text{50 seconds}}$.Person ${\text{3}}$ starts out southward from point S and runs all the way around the track, finishing at point S in ${\text{50 seconds}}$.
Rank these three people according to the magnitude of their average velocities during their movements on the track, greatest magnitude first.
A. $3,2,1$
B. $1,2,3$
C. ${\text{1}}$ and ${\text{2}}$ tie, then ${\text{3}}$
D. ${\text{3}}$, then ${\text{1}}$ and ${\text{2}}$ tie
E. All tie

Answer 1

We are asked to find the rank of the three people from greatest average velocity to smallest. First, draw the diagram of the given track to visualize the problem. Then use the formula of average velocity to find the average velocities of the three persons separately then compare their velocities and form the required rank.

Complete step by step answer:
Given, there is a track whose circumference is $400\,{\text{m}}$.The straight portions are of length $100\,{\text{m}}$.The curved portions are of length $100\,{\text{m}}$.Three persons ${\text{1}}$, ${\text{2}}$ and ${\text{3}}$ move on the track.Let us draw a diagram of the track,

We have the formula for average velocity as,
${v_{av}} = \dfrac{{{\text{Total displacement}}}}{{{\text{total time}}}}$ (i)
Now, let us check the path of each person
Person ${\text{1}}$ starts from point S and moves in north direction for $100\,{\text{m}}$ and reaches point F in ${\text{50 seconds}}$
Total displacement is, $100\,{\text{m}}$ and total time taken is ${\text{50 seconds}}$ so, using the formula from equation (i), we have the average velocity of person ${\text{1}}$ as,
${v_{av1}} = \dfrac{{100\,{\text{m}}}}{{50\,{\text{s}}}} = 2\,{\text{m}}{{\text{s}}^{{\text{ - 1}}}}$
Person ${\text{2}}$ starts from point S and moves southward and reaches point F in ${\text{50 seconds}}$
Total displacement here is, $100\,{\text{m}}$ and total time taken is ${\text{50 seconds}}$ so, using the formula from equation (i), we have the average velocity of person $2$ as,
${v_{av2}} = \dfrac{{100\,{\text{m}}}}{{50\,{\text{s}}}} = 2\,{\text{m}}{{\text{s}}^{{\text{ - 1}}}}$
Person ${\text{3}}$ starts from point S runs all the way around the track and reaches point S in ${\text{50 seconds}}$
Total displacement here is, $0\,{\text{m}}$and total time taken is ${\text{50 seconds}}$ so, using the formula from equation (i), we have the average velocity of person $3$ as,
${v_{av2}} = \dfrac{{0\,{\text{m}}}}{{50\,{\text{s}}}} = 0\,{\text{m}}{{\text{s}}^{{\text{ - 1}}}}$.
Therefore average velocities of person ${\text{1}}$, $2$ and $3$ are $2\,{\text{m}}{{\text{s}}^{{\text{ - 1}}}}$, $2\,{\text{m}}{{\text{s}}^{{\text{ - 1}}}}$ and $0\,{\text{m}}{{\text{s}}^{{\text{ - 1}}}}$.
So, the rank of the three people from greatest average velocity to smallest is ${\text{1}}$ and ${\text{2}}$ tie, then ${\text{3}}$.

Hence the correct answer is option C.

Note: Most of the time students get confused between displacement and distance covered, always remember distance covered is the total length covered by a body and displacement is the shortest distance between the initial and final position. If in this problem you take the distance covered instead of displacement for average velocity you will get an incorrect answer. Remember displacement per unit time is known as velocity and distance covered per unit time is known as speed.