Q. No.The velocity \(v\) of an object varies with its position \(x\) on a straight line as \(v=3\sqrt{x}.\) Its acceleration versus time \((a\text-t)\) graph is best represented by:
1.
2.
3.
4.
Starting from rest, a car accelerates uniformly at the rate of \(1~\text{m/s}^2\) for some time, then decelerates uniformly at the rate of \(2~\text{m/s}^2\) and finally comes to rest after a journey of \(1\) minute. The maximum possible speed of the car during this journey is:
1. \(10\) m/s
2. \(20\) m/s
3. \(30\) m/s
4. \(40\) m/s
A particle is moving along the \(x\)-axis such that its velocity varies with time as per the equation \(v = 20\left(1-\frac{t}{2}\right) \). At \(t=0 \) particle is at the origin. From the following, select the correct position \((x)\) - time \((t)\) plot for the particle:
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Suppose you are riding a bike with a speed of \(20~\text{m/s}\) due east relative to a person \(A\) who is walking on the ground towards the east. If your friend \(B\) walking on the ground due west measures your speed as \(30~\text{m/s}\) due east, then the relative velocity between two reference frames \(A\) and \(B\) is:
| 1. | the velocity of \(A\) with respect to \(B\) is \(5~\text{m/s}\) towards the east. |
| 2. | the velocity of \(A\) with respect to \(B\) is \(5~\text{m/s}\) towards the west. |
| 3. | the velocity of \(A\) with respect to \(B\) is \(10~\text{m/s}\) towards the east. |
| 4. | the velocity of \(A\) with respect to \(B\) is \(10~\text{m/s}\) towards the west. |
A helicopter moving vertically upwards releases a packet when it is at a certain height above the ground. The packet initially moves upwards for a time \(t_1\) and then falls downwards for a time \(t_2\) until it reaches the ground. Then:
| 1. | \(t_1<t_2\) | 2. | \(t_1=t_2\) |
| 3. | \(t_1>t_2\) | 4. | Data insufficient |
Two stones are thrown vertically up simultaneously with different velocities. Which of the following graphs represents the relative separation \((\Delta y)\) between them as a function of time \((t)\)?
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The graph below shows position as a function of time for two trains running on parallel tracks.
Which of the following statements is true?
| 1. | At time \(t_B \) both the trains have the same velocity |
| 2. | Both the trains have the same velocity at some time after \(t_B \) |
| 3. | Both the trains have the same velocity at some time before \(t_B \) |
| 4. | Both the trains have the same acceleration |
A particle is moving along the positive \(x\)-axis with some initial velocity. The acceleration-time graphs are shown. In which case the velocity of the particle will increase for the entire time between \(t_1\) and \(t_2\)?
| 1. | only in (II) |
| 2. | in (I) and (III) |
| 3. | in (I) and (II) |
| 4. | in (I), (II) and (III) |
A particle is allowed to fall from rest from a height \(h\). Which of the following represents its velocity versus time graph?
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A body is moving along a straight line according to the equation of motion, \(x= t^{2} - 3 t + 4\), where \(x\) is in metre and \(t\) is in seconds. What is the acceleration of the body when it comes to rest?
| 1. | zero | 2. | \(2~\text{m/s}^2\) |
| 3. | \(\frac{3}{2}~\text{m/s}^2\) | 4. | \(1~\text{m/s}^2\) |
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