TS EAMCET · Physics · Motion In Two Dimensions

A cyclist traversed half the distance of a linear track with a velocity $10 m s^{- 1} .$ The remaining part of the track was covered with a velocity $v_{1}$ for half the time and a velocity $v_{2}$ for the other half of the time. If $v_{1} + v_{2} = 20 m s^{- 1},$ then the average velocity of the cyclist during the completion of the journey through the track is

A $30 m s^{- 1}$
B $20 m s^{- 1}$
C $10 m s^{- 1}$
D $15 m s^{- 1}$

Verified Solution

Answer & Solution

Correct Answer

(C) $10 m s^{- 1}$

Step-by-step Solution

Detailed explanation

Let the complete distance of the track is, 4x Time of completion of half the distance is given by, t1=2x10 Time of completion of remaining by v1 is, T2 Time of completion of remaining by v2 is, T2 Average velocity for last half distance is, vavg=V1T2+V2T2T…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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