Question:
A car travels first half of the distance with a velocity \(V\) and second half of the distance with a velocity \(3V\), then the average velocity is
A car travels first half of the distance with a velocity \(V\) and second half of the distance with a velocity \(3V\), then the average velocity is
Show Hint
For equal distances covered at speeds \(v_1\) and \(v_2\), use
\[
v_{\text{avg}}
=
\frac{2v_1v_2}{v_1+v_2}.
\]
Here,
\[
v_{\text{avg}}
=
\frac{2(V)(3V)}{V+3V}
=
\frac{3V}{2}.
\]
Updated On: Jul 29, 2026
- \(2V\)
- \(3V\)
- \(4V\)
- \(1.5V\)
Show Solution
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The Correct Option is D
Solution and Explanation
Concept:
When equal distances are covered with different velocities \(v_1\) and \(v_2\), the average velocity is the harmonic mean:
\[
v_{\text{avg}}
=
\frac{2v_1v_2}{v_1+v_2}.
\]
Step 1: Assume the total distance is \(2d\). Then, \[ \text{First half distance}=d, \qquad \text{Second half distance}=d. \] Velocity during first half: \[ V. \] Velocity during second half: \[ 3V. \]
Step 2: Calculate the total time taken. Time for first half: \[ t_1=\frac{d}{V}. \] Time for second half: \[ t_2=\frac{d}{3V}. \] Therefore, \[ T=t_1+t_2 = \frac{d}{V}+\frac{d}{3V} = \frac{4d}{3V}. \]
Step 3: Calculate the average velocity. Total distance travelled: \[ 2d. \] Hence, \[ v_{\text{avg}} = \frac{\text{Total Distance}} {\text{Total Time}} = \frac{2d}{\frac{4d}{3V}}. \] \[ = \frac{3V}{2}. \] \[ =1.5V. \] Therefore, \[ \boxed{v_{\text{avg}}=\frac{3V}{2}=1.5V} \] \[ \boxed{\text{Answer = (D)}} \]
Step 1: Assume the total distance is \(2d\). Then, \[ \text{First half distance}=d, \qquad \text{Second half distance}=d. \] Velocity during first half: \[ V. \] Velocity during second half: \[ 3V. \]
Step 2: Calculate the total time taken. Time for first half: \[ t_1=\frac{d}{V}. \] Time for second half: \[ t_2=\frac{d}{3V}. \] Therefore, \[ T=t_1+t_2 = \frac{d}{V}+\frac{d}{3V} = \frac{4d}{3V}. \]
Step 3: Calculate the average velocity. Total distance travelled: \[ 2d. \] Hence, \[ v_{\text{avg}} = \frac{\text{Total Distance}} {\text{Total Time}} = \frac{2d}{\frac{4d}{3V}}. \] \[ = \frac{3V}{2}. \] \[ =1.5V. \] Therefore, \[ \boxed{v_{\text{avg}}=\frac{3V}{2}=1.5V} \] \[ \boxed{\text{Answer = (D)}} \]
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