Average Velocity

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A car covers first half of a distance at speed v1 and second half at speed v2. Average speed is:

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(v1+v2)/2

2 v1 v2 /(v1+v2)

$(v 1^{2} + v 2^{2}) / (v 1 + v 2)$

(v1 v2)/(v1+v2)

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About This Question

Subject: physics
Chapter: kinematics
Topic: average velocity
Difficulty: Medium
Year: 2025

Solution

Correct Answer:

2 v1 v2 /(v1+v2)

Let the total distance be $2 D$ .

Time taken for the first half: $t_{1} = \frac{D}{v _{1}}$ .
Time taken for the second half: $t_{2} = \frac{D}{v _{2}}$ .
Total time $T_{t o t a l} = t_{1} + t_{2} = \frac{D}{v _{1}} + \frac{D}{v _{2}} = D (\frac{v _{1} + v _{2}}{v _{1} v _{2}})$ .
Average speed $v_{a vg} = \frac{Total Distance}{Total Time} = \frac{2 D}{D ( \frac{v _{1} + v _{2}}{v _{1} v _{2}} )} = \frac{2 v _{1} v _{2}}{v _{1} + v _{2}}$ . This is the harmonic mean of the two speeds.

This medium difficulty physics question is from the chapter kinematics, covering the topic of average velocity. It appeared in the 2025 exam.

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Average Velocity

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