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Q. No.A car travels a distance \(AB\) in three equal segments: the first third at a velocity of \(v_1~\text{m/s},\) the second third at \(v_2~\text{m/s},\) and the final third at \(v_3~\text{m/s}.\) Given that \(v_3 = 3v_1 , ~v_2 = 2v_1\) and \(v_1 = 11~\text{m/s} ,\) the average velocity of the car is:
| 1. | \(12~\text{m/s}\) | 2. | \(18~\text{m/s}\) |
| 3. | \(16~\text{m/s}\) | 4. | \(11~\text{m/s}\) |
Subtopic: Â Average Speed & Average Velocity |
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A car moving on a straight-line travels in same direction half of the distance with uniform velocity \(v_1\) and other half of the distance with uniform velocity \(v_2.\) The average velocity of the car is equal to:
1. \(\dfrac{2v_1v_2}{v_1+v_2}\)
2. \(\dfrac{v_1+v_2}{2}\)
3. \(v_1+v_2\)
4. \(\sqrt{v_1+v_2}\)
1. \(\dfrac{2v_1v_2}{v_1+v_2}\)
2. \(\dfrac{v_1+v_2}{2}\)
3. \(v_1+v_2\)
4. \(\sqrt{v_1+v_2}\)
Subtopic: Â Average Speed & Average Velocity |
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A car travels \(4\text{ km}\) distance with a speed of \(3\text{ km/h}\) and next \(4\text{ km}\) with a speed of \(5\text{ km/h}.\) What is the average speed of the car?
1. \(\dfrac{15}{2}\text{ km/hr}\)
2. \(\dfrac{15}{4}\text{ km/hr}\)
3. \(15\text{ km/hr}\)
4. \(10\text{ km/hr}\)
1. \(\dfrac{15}{2}\text{ km/hr}\)
2. \(\dfrac{15}{4}\text{ km/hr}\)
3. \(15\text{ km/hr}\)
4. \(10\text{ km/hr}\)
Subtopic: Â Average Speed & Average Velocity |
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A particle moves from \(A\) to \(B\) via \(C\) with uniform speed of \(\pi\) m/s. The average velocity during the journey is:
1. \(\sqrt{3}\text{ m/s}\)
2. \(\dfrac{\sqrt{3}}{2}\text{ m/s}\)
3. \(\dfrac{3\sqrt{3}}{2}\text{ m/s}\)
4. \(2\text{ m/s}\)
1. \(\sqrt{3}\text{ m/s}\)
2. \(\dfrac{\sqrt{3}}{2}\text{ m/s}\)
3. \(\dfrac{3\sqrt{3}}{2}\text{ m/s}\)
4. \(2\text{ m/s}\)
Subtopic: Â Average Speed & Average Velocity |
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An object travels a distance \(x\) with a constant speed \(v_1,\) and then covers another equal distance \(x \) with a different constant speed \(v_2.\) The average velocity \(v\) for the entire journey is given by:
| 1. | \(v=\left(\dfrac{v_1+v_2}{2}\right) \) | 2. | \(\dfrac{1}{v}=\dfrac{1}{v_1}+\dfrac{1}{v_2} \) |
| 3. | \(v=\left(\dfrac{2 v_1 v_2}{v_1+v_2}\right) \) | 4. | \(v=\left(\dfrac{v_1-v_2}{2}\right) \) |
Subtopic: Â Average Speed & Average Velocity |
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A train starting from rest first accelerates uniformly up to a speed of \(80 ~\text {km/h}\) for time \(t\), then it moves with a constant speed for time \(3t.\) The average speed of the train for this duration of the journey will be (in \(\text{km/h}\)):
1. 30
2. 80
3. 40
4. 70
1. 30
2. 80
3. 40
4. 70
Subtopic: Â Average Speed & Average Velocity |
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A particle moving in a straight line covers half the distance with speed \(\begin{equation} 6 \mathrm{~m} / \mathrm{s} \end{equation}\). The other half is covered in two equal time intervals with speeds \(\begin{equation} 9 \mathrm{~m} / \mathrm{s} \end{equation}\) and \(\begin{equation} 15 \mathrm{~m} / \mathrm{s} \end{equation}\) respectively. The average speed of the particle during the motion is :
1. \(\begin{equation} 8.8 \mathrm{~m} / \mathrm{s} \end{equation}\)
2. \(\begin{equation} 8 \mathrm{~m} / \mathrm{s} \end{equation}\)
3. \(\begin{equation} 9.2 \mathrm{~m} / \mathrm{s} \end{equation}\)
4. \(\begin{equation} 10 \mathrm{~m} / \mathrm{s} \end{equation}\)
1. \(\begin{equation} 8.8 \mathrm{~m} / \mathrm{s} \end{equation}\)
2. \(\begin{equation} 8 \mathrm{~m} / \mathrm{s} \end{equation}\)
3. \(\begin{equation} 9.2 \mathrm{~m} / \mathrm{s} \end{equation}\)
4. \(\begin{equation} 10 \mathrm{~m} / \mathrm{s} \end{equation}\)
Subtopic: Â Average Speed & Average Velocity |
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