Q. No.Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Acceleration |
70%
Level 2: 60%+
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The position of a particle as a function of time \(t\), is given by;
\(x(t)=a t+b t^2-c t^3\)
where \(a\), \(b\) and \(c\) are constants. When the particle attains zero acceleration, then its velocity will be:
1. \( a+\frac{b^2}{4 c} \)
2. \( a+\frac{b^2}{c} \)
3. \( a+\frac{b^2}{3 c} \)
4. \( a+\frac{b^2}{2 c}\)
Subtopic: Acceleration |
84%
Level 1: 80%+
JEE
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A particle is moving in a straight line such that its velocity is increasing at \(5\) ms-1 per meter. The acceleration of the particle at a point where its velocity is \(20\) ms-1, is:
1. \(100\) ms-2
2. \(200\) ms-2
3. \(300\) ms-2
4. \(400\) ms-2
1. \(100\) ms-2
2. \(200\) ms-2
3. \(300\) ms-2
4. \(400\) ms-2
Subtopic: Acceleration |
74%
Level 2: 60%+
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A train (moving with initial speed = \(20\) m/s) applies brakes to stop at the incoming station which is \(500\) m ahead. If brakes are applied after moving \(250\) m, then how much beyond the station train would stop?
1. \(125\) m
2. \(500\) m
3. \(250\) m
4. \(400\) m
1. \(125\) m
2. \(500\) m
3. \(250\) m
4. \(400\) m
Subtopic: Acceleration |
72%
Level 2: 60%+
JEE
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Given below are two statements:
| Statement I: | We can get displacement from the acceleration-time graph. |
| Statement II: | We can get acceleration from the velocity-time graph. |
| 1. | Both Statement I and Statement II are correct. |
| 2. | Both Statement I and Statement II are incorrect. |
| 3. | Statement I is correct and Statement II is incorrect. |
| 4. | Statement I is incorrect and Statement II is correct. |
Subtopic: Acceleration |
68%
Level 2: 60%+
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In a straight-road car race, car \({A}\) reaches the finish line \(t\) seconds earlier than car \({B}\) and has a final speed \(v\) greater than the speed of car \({B}.\) Both cars start from rest and move with constant accelerations \(a_1\) and \(a_2\) respectively. Then, \(v\) is equal to:
| 1. | \(\dfrac{2a_1a_1 }{a_1+a_2}~{t}\) | 2. | \(\sqrt{2a_1a_2}~{t}\) |
| 3. | \(\sqrt{a_1a_2}~{t} \) | 4. | \(\dfrac{a_1+a_2 }{2}~{t}\) |
Subtopic: Acceleration |
Level 3: 35%-60%
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The distance \(x\) covered by a particle in one-dimensional motion varies with time \(t\) as \(x^2=at^2+2bt+c.\) The acceleration of the particle depends on:
1. \(x^{-3} \)
2. \(x^{-5} \)
3. \(x^{-6} \)
4. \(x^{-1} \)
1. \(x^{-3} \)
2. \(x^{-5} \)
3. \(x^{-6} \)
4. \(x^{-1} \)
Subtopic: Acceleration |
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A car accelerates from rest at a constant rate \(\alpha\) for some time, after which it decelerates at a constant rate \(\beta\) to come to rest. If the total time elapsed is \(t~\text{seconds},\) then the total distance traveled is:
1. \(\dfrac{4 \alpha \beta}{(\alpha+\beta)} t^2\)
2. \(\dfrac{\alpha \beta}{4(\alpha+\beta)} t^2\)
3. \(\dfrac{2 \alpha \beta}{(\alpha+\beta)} t^2\)
4. \(\dfrac{\alpha \beta}{2(\alpha+\beta)} t^2\)
1. \(\dfrac{4 \alpha \beta}{(\alpha+\beta)} t^2\)
2. \(\dfrac{\alpha \beta}{4(\alpha+\beta)} t^2\)
3. \(\dfrac{2 \alpha \beta}{(\alpha+\beta)} t^2\)
4. \(\dfrac{\alpha \beta}{2(\alpha+\beta)} t^2\)
Subtopic: Acceleration |
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The relation between time \({t}\) and distance \({x}\) for a moving body is given as \({t=mx^2+nx},\) where \(m\) and \(n\) are constants. The retardation of the motion is:
(Where \(v\) stands for velocity)
1. \({2n^2v^2}\)
2. \({2mnv^3}\)
3. \({2mv^3}\)
4. \({2nv^3}\)
(Where \(v\) stands for velocity)
1. \({2n^2v^2}\)
2. \({2mnv^3}\)
3. \({2mv^3}\)
4. \({2nv^3}\)
Subtopic: Acceleration |
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If the velocity of a body related to displacement \({x}\) is given by \(v=\sqrt{5000+24 x}~\text{m/s},\) then the acceleration of the body is:
1. \(3~\text{m/s}^2\)
2. \(6~\text{m/s}^2\)
3. \(9~\text{m/s}^2\)
4. \(12~\text{m/s}^2\)
1. \(3~\text{m/s}^2\)
2. \(6~\text{m/s}^2\)
3. \(9~\text{m/s}^2\)
4. \(12~\text{m/s}^2\)
Subtopic: Acceleration |
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