For the given acceleration \(\left ( a \right )\) versus time \(\left ( t \right )\) graph of a body, the body is initially at rest.

       
From the following, the velocity \(\left ( v \right )\) versus time \(\left ( t \right )\) graph will be:

1.   2.  
3.   4.  

Subtopic:  Non Uniform Acceleration |
 61%
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A particle moves with a velocity \(v = αt^{3}\) along a straight line. The average speed in time interval \(t=0\) to \(t=T\) will be:
1. \(\alpha T^3\)
2. \(\frac{αT^{3}}{2}\)
3. \(\frac{\alpha T^3}{3}\)
4. \(\frac{αT^{3}}{4}\)

Subtopic:  Average Speed & Average Velocity |
 60%
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The position (\(x\)) of a particle in a straight line motion is given by \(x = 2 + 10 t - 5 t^{2}~\text{m}\). Its velocity (\(v\)) is best represented by?

1. 2.
3. 4.
Subtopic:  Graphs |
 76%
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The displacement \((x)\) of a point moving in a straight line is given by; \(x=8t^2-4t.\) Then the velocity of the particle is zero at:

1. \(0.4\) s 2. \(0.25\) s
3. \(0.5\) s 4. \(0.3\) s
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 87%
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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. \(1~\text{m/s}^2\)

Subtopic:  Acceleration |
 84%
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A particle is allowed to fall from rest from a height \(h\). Which of the following represents its velocity versus time graph?

1. 2.
3. 4.

Subtopic:  Uniformly Accelerated Motion |
 60%
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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)

Subtopic:  Graphs |
From NCERT
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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
Subtopic:  Graphs |
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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 \((t)\)?

1. 2.
3. 4.
Subtopic:  Graphs |
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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.   
Subtopic:  Acceleration |
 61%
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