A body is projected vertically upward and then allowed to fall back down under gravity. Which of the following velocity–time \((v \text-t) \) graphs correctly represents its motion throughout the ascent and descent?

1. 2.
3. 4.
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The velocity-time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance travelled by the car and the scooter in \(15 ~\text{s}\) and, (ii) the time at which the car will catch up with the scooter respectively are:

1. \(112.5\text{ m and}~ 22.5~ \text{s} \)
2. \(337.5\text{ m and}~ 25~ \text{s} \)
3. \(225.5\text{ m and}~ 10~ \text{s} \)
4. \(112.5\text{ m and}~ 15~ \text{s} \)
Subtopic:  Graphs |
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A ball is thrown vertically up (taken as \(+z\)-axis) from the ground. The correct momentum\(\text-\)height (\(p\text{-}h\)) diagram is:

1.   2.  
3.   4.  


 

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A tennis ball is released from a height \(h\) and after freely falling on a wooden floor it rebounds and reaches height \(\frac{h}{2}\). The velocity versus height of the ball during its motion may be represented graphically by:
(graph are drawn schematically and on not to scale)

1. 2.  
3.   4.  
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The velocity (\(v\)) and time (\(t\)) graph of a body in a straight-line motion is shown in the figure. The point \(S\) occurs at \(4.333\) seconds. The total distance covered by the body in \(6\) s is:

       
1. \(12\) \(\text{m}\)
2. \(\dfrac{49}{12}\) \(\text{m}\)
3. \(11\) \(\text{m}\)
4. \(\dfrac{37}{3}\) \(\text{m} \)

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If the velocity-time graph has the shape \(AMB,\) what would be the shape of the corresponding acceleration-time graph?

 

1.   2.  
3.   4.  

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A scooter accelerates from rest for time \(t_1\) at constant rate \(a_1\) and then retards at constant rate \(a_2\) for time \(t_2\) and comes to rest. The correct value of  \(\frac{t_1}{t_2}\) will be:
1. \(\frac{a_1+a_2}{a_2}\)
2. \(\frac{a_2}{a_1}\)
3. \(\frac{a_1}{a_2}\)
4. \(\frac{a_1+a_2}{a_1}\)

Subtopic:  Graphs |
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A bullet is shot vertically downwards with an initial velocity of \(100\) m/s from a certain height. Within \(10\) s, the bullet reaches the ground and instantaneously comes to rest due to the perfectly inelastic collision. The velocity-time curve for total time \(t=20\) s will be : (Take \(g=10\) m/s2 )
1.   2.
3. 4.
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The position-time graph for a particle is parabolic (as shown in the figure).
   
Choose the corresponding \((v\text-t)\) graph.
 
1. 2.
3. 4.
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The graph shows the position-time \((x\text-t)\) relation for two students, \(\mathrm{A}\) and \(\mathrm{B}\) from school to their home.

  
a. \(\mathrm{A}\) is faster than \(\mathrm{B}\)
b. \(\mathrm{B}\) is faster than \(\mathrm{A}\)
c. \(\mathrm{B}\) lives further away than \(\mathrm{A}\)
d. \(\mathrm{A}\) live further away than \(\mathrm{B}\)

Choose the correct entries:
1. (a), (d)
2. (b), (c)
3. (b), (d)
4. (a), (c)
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