Question:
A car travelling on a straight track moves with uniform velocity \(v_1\) for some time and with uniform velocity \(v_2\) for the next equal time. The average velocity of the car is
A car travelling on a straight track moves with uniform velocity \(v_1\) for some time and with uniform velocity \(v_2\) for the next equal time. The average velocity of the car is
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For equal time intervals, average velocity is arithmetic mean of velocities.
Updated On: Apr 23, 2026
- \(\frac{v_1v_2}{2}\)
- \(\frac{v_1v_2}{4}\)
- \(\frac{v_1 + v_2}{2}\)
- \(\frac{v_1 - v_2}{2}\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
Average velocity = \(\frac{\text{Total displacement}}{\text{Total time}}\).
Step 2: Detailed Explanation:
Let each time interval be \(t\). Displacement in first interval = \(v_1t\), in second = \(v_2t\).
Total displacement = \(v_1t + v_2t = t(v_1 + v_2)\). Total time = \(2t\).
Average velocity = \(\frac{t(v_1 + v_2)}{2t} = \frac{v_1 + v_2}{2}\).
Step 3: Final Answer:
Thus, average velocity = \(\frac{v_1 + v_2}{2}\).
Average velocity = \(\frac{\text{Total displacement}}{\text{Total time}}\).
Step 2: Detailed Explanation:
Let each time interval be \(t\). Displacement in first interval = \(v_1t\), in second = \(v_2t\).
Total displacement = \(v_1t + v_2t = t(v_1 + v_2)\). Total time = \(2t\).
Average velocity = \(\frac{t(v_1 + v_2)}{2t} = \frac{v_1 + v_2}{2}\).
Step 3: Final Answer:
Thus, average velocity = \(\frac{v_1 + v_2}{2}\).
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