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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 |
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Level 2: 60%+
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Two buses \(P\) and \(Q\) start from a point at the same time and move in a straight line. 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. | \(\dfrac{\alpha-f}{1+\beta} \) | 2. | \(\dfrac{\alpha+f}{2(\beta-1)} \) |
| 3. | \(\dfrac{\alpha+f}{2(1+\beta)} \) | 4. | \(\dfrac{f-\alpha}{2(1+\beta)}\) |
Subtopic: Instantaneous Speed & Instantaneous Velocity |
87%
Level 1: 80%+
Hints
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 |
93%
Level 1: 80%+
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 |
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Level 1: 80%+
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If position of particle is changing with time as \(r=(t^2-2t)\text{ m}. \) The velocity of the particle at \(t = 2\text{ s} \) is:
1. \(2\text{ m/s} \)
2. \(3\text{ m/s}\)
3. \(0\text{ m/s} \)
4. \(4\text{ m/s}\)
1. \(2\text{ m/s} \)
2. \(3\text{ m/s}\)
3. \(0\text{ m/s} \)
4. \(4\text{ m/s}\)
Subtopic: Instantaneous Speed & Instantaneous Velocity |
91%
Level 1: 80%+
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A particle moves along a straight line, and its displacement at time \(t\) seconds is given by:
\(s= (2t^2 + 5) ~\text{m}\)
What is the velocity of the particle at \(t=1~\text{s?}\)
| 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 |
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Level 1: 80%+
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