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Q. No.A particle is moving with speed \(v=b\sqrt{x} \) along the positive \(x \)-axis. The speed of the particle at time \(t=T\) is: (assume that the particle is at origin at \(t=0 \))
| 1. | \(\dfrac{b^2T}{\sqrt{2}}\) | 2. | \(b^2T\) |
| 3. | \(\dfrac{b^2T}{2}\) | 4. | \(\dfrac{b^2T}{4}\) |
Subtopic: Instantaneous Speed & Instantaneous Velocity |
63%
From NCERT
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Two buses \(P\) and \(Q\) start from a point at the same time and move in a straight line and their positions are represented by \(X_p(t)=\alpha t+\beta t^2 \) and \(X_{Q}(t)=ft-t^2 \). At what time, do both the buses have the same velocity?
| 1. | \(\frac{\alpha-f}{1+\beta} \) | 2. | \(\frac{\alpha+f}{2(\beta-1)} \) |
| 3. | \(\frac{\alpha+f}{2(1+\beta)} \) | 4. | \(\frac{f-\alpha}{2(1+\beta)}\) |
Subtopic: Instantaneous Speed & Instantaneous Velocity |
89%
From NCERT
JEE
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What will be the velocity of the particle if the position of the particle is given by; \(x =2t^{2}\) at \(t=2~\text s?\)
1. \(8~\text{m/s}\)
2. \(4~\text{m/s}\)
3. \(16~\text{m/s}\)
4. \(32~\text{m/s}\)
1. \(8~\text{m/s}\)
2. \(4~\text{m/s}\)
3. \(16~\text{m/s}\)
4. \(32~\text{m/s}\)
Subtopic: Instantaneous Speed & Instantaneous Velocity |
94%
From NCERT
JEE
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The position \(x\) of a particle moving along the \(x\text-\)axis varies with time \(t\) according to the equation: \(x=2.5t^2.\) What is the speed of the particle at \(t=5\) s?
| 1. | \(5\) m/s | 2. | \(10\) m/s |
| 3. | \(25\) m/s | 4. | \(50\) m/s |
Subtopic: Instantaneous Speed & Instantaneous Velocity |
87%
From NCERT
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If position of particle is changing with time as r = t2 – 2t (m). Find the velocity at t = 2 second
1. 2 m/s
2. 3 m/s
3. 0 m/s
4. 4 m/s
1. 2 m/s
2. 3 m/s
3. 0 m/s
4. 4 m/s
Subtopic: Instantaneous Speed & Instantaneous Velocity |
92%
From NCERT
JEE
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A particle is moving in one dimension, its displacement-time relation is given as \(S= (2t^2 + 5)\) where \(S\) is in meters and \(t\) is in seconds. Find its velocity (in \(\text{m/s}\)) at \(t =1\) second.
1. \(4~\text{m/s}\)
2. \(2~\text{m/s}\)
3. \(6~\text{m/s}\)
4. \(7~\text{m/s}\)
1. \(4~\text{m/s}\)
2. \(2~\text{m/s}\)
3. \(6~\text{m/s}\)
4. \(7~\text{m/s}\)
Subtopic: Instantaneous Speed & Instantaneous Velocity |
94%
From NCERT
JEE
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