The figure gives the \((x\text-t)\) plot of a particle in a one-dimensional motion. Three different equal intervals of time are shown. The signs of average velocity for each of the intervals \(1,\) \(2\) & \(3,\) respectively are:

               

1. \(-,-,+\)
2. \(+,-,+\)
3. \(-,+,+\)
4. \(+,+,-\)

Subtopic:  Average Speed & Average Velocity |
 89%
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A car moves with a speed of \(60\) km/h for \(1\) hour in the east direction and with the same speed for \(30\) min in the south direction. The displacement of the car from the initial position is:

1. \(60\) km 2. \(30 \sqrt{2}\)  km
3. \(30 \sqrt{5}\) km 4. \(60 \sqrt{2}\) km
Subtopic:  Distance & Displacement |
 69%
From NCERT
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A drunkard walking in a narrow lane takes \(5\) steps forward and \(3\) steps backward, followed again by \(5\) steps forward and \(3\) steps backward, and so on. Each step is \(1\) m long and requires \(1\) s. There is a pit on the road \(13\) m away from the starting point. The drunkard will fall into the pit after:
1. \(37\) s
2. \(31\) s
3. \(29\) s
4. \(33\) s

Subtopic:  Distance & Displacement |
 62%
From NCERT
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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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The displacement \(x\) of a particle varies with time \(t\) as \(x = ae^{-\alpha t}+ be^{\beta t}\)
, where \(a,\) \(b,\) \(\alpha,\) and \(\beta\) are positive constants. The velocity of the particle will:

1. be independent of \(\alpha\) and \(\beta.\)
2. go on increasing with time.
3. drop to zero when \(\alpha=\beta.\)
4. go on decreasing with time.
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 52%
From NCERT
AIPMT - 2005
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If a body travels some distance in a given time interval, then for that time interval, its:

1. Average speed  ≥  |Average velocity|
2. |Average velocity|  ≥  Average speed
3. Average speed < |Average velocity|
4. |Average velocity| must be equal to average speed. 

Subtopic:  Average Speed & Average Velocity |
 83%
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A particle moves along a path \(ABCD\) as shown in the figure. The magnitude of the displacement of the particle from \(A\) to \(D\) is:

       

1. (5+102)m
2. \(10\) m
3. 152 m
4. \(15\) m

Subtopic:  Distance & Displacement |
 70%
From NCERT
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When brakes are applied to a moving vehicle, the distance it travels before stopping is called stopping distance. It is an important factor for road safety and depends on the initial velocity \(\mathrm{v_0}\) and the braking capacity, or deceleration, \(-a\) that is caused by the braking. Expression for stopping distance of a vehicle in terms of \(\mathrm{v_0}\) and \(a\) is:
1. \(\frac{\mathrm{v_o}^2}{2a}\)
2. \(\frac{\mathrm{v_o}}{2a}\)
3. \(\frac{\mathrm{v_o}^2}{a}\)
4. \(\frac{2a}{\mathrm{v_o}^2}\)

Subtopic:  Acceleration |
 82%
From NCERT
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The position of an object moving along the x-axis is given by, \(x=a+bt^2\)  where \(a=8.5\) m, \(b=2.5\) ms-2and \(t\) is measured in seconds. Its velocity at \(t=2.0\) s will be:
1. \(13\) m/s
2. \(17\) m/s
3. \(10\) m/s
4. \(0\) 

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 86%
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The figure shows the displacement-time graph of a particle moving on the x-axis. Then,                           

                  

1. the particle is continuously going in a positive x-direction.
2. the particle is at rest.
3. the velocity increases up to a time \(t_0\), and then becomes constant.
4. the particle moves at a constant velocity up to a time \(t_0\), and then stops.

Subtopic:  Graphs |
 69%
From NCERT
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