Q. No.The equation of motion of a particle is given by \(x =a\sin\left(50t+ \dfrac{\pi}{3}\right)~\text{cm}.\) The particle will come to rest at time \(t_1\) and it will have zero acceleration at time \(t_2\). The \(t_1\) and \(t_2\) respectively are:
1. \(\dfrac{\pi}{300} ~\text{s}, \dfrac{\pi}{75} ~\text{s} \)
2. \( \dfrac{\pi}{75} ~\text{s}, \dfrac{\pi}{300} ~\text{s}\)
3. \( \dfrac{\pi}{300} ~\text{s}, \dfrac{\pi}{25} ~\text{s}\)
4. \( \dfrac{\pi}{50} ~\text{s}, \dfrac{\pi}{100} ~\text{s}\)
1. \(\dfrac{\pi}{300} ~\text{s}, \dfrac{\pi}{75} ~\text{s} \)
2. \( \dfrac{\pi}{75} ~\text{s}, \dfrac{\pi}{300} ~\text{s}\)
3. \( \dfrac{\pi}{300} ~\text{s}, \dfrac{\pi}{25} ~\text{s}\)
4. \( \dfrac{\pi}{50} ~\text{s}, \dfrac{\pi}{100} ~\text{s}\)
Subtopic: Acceleration |
70%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
A particle of mass \(m\) falls from rest through a resistive medium having resistive force, \(F = -kv\), where \(v\) is the velocity of the particle and \(k\) is a constant. Which of the following graphs represents velocity \((v)\) versus time \((t)\)?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Acceleration |
59%
Level 3: 35%-60%
Please attempt this question first.
Hints
Please attempt this question first.
A particle moves along the \(𝑥\text-\)axis and has its displacement \(x \) varying with time \(t\) according to the equation:
\(x=c_0\left(t^2-2\right)+c(t-2)^2 \)
where \(c_0\) and \(c \) are constants of appropriate dimensions. Then, which of the following statements is correct?
\(x=c_0\left(t^2-2\right)+c(t-2)^2 \)
where \(c_0\) and \(c \) are constants of appropriate dimensions. Then, which of the following statements is correct?
| 1. | the acceleration of the particle is \(2(c+c_0) \) |
| 2. | the initial velocity of the particle is \(4c\) |
| 3. | the acceleration of the particle is \(2c_0\) |
| 4. | the acceleration of the particle is \(2c\) |
Subtopic: Acceleration |
75%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
A particle moves in a straight line so that its displacement \(x\) at any time \(t\) is given by \(x^2 = 1+t^2.\) Its acceleration at any time t is \(x^{-n}\) where \(n\) = _______.
1. \(-3\)
2. \(+3\)
3. \(+1\)
4. \(-1\)
1. \(-3\)
2. \(+3\)
3. \(+1\)
4. \(-1\)
Subtopic: Acceleration |
Level 4: Below 35%
Please attempt this question first.
Hints
Please attempt this question first.
If the velocity of the particle is given by \({v=4\sqrt{x}}.\) Then the acceleration of the particle is:
1. \({2~\text{m/s}^2}\)
2. \({4~\text{m/s}^2}\)
3. \({8~\text{m/s}^2}\)
4. \({16~\text{m/s}^2}\)
1. \({2~\text{m/s}^2}\)
2. \({4~\text{m/s}^2}\)
3. \({8~\text{m/s}^2}\)
4. \({16~\text{m/s}^2}\)
Subtopic: Acceleration |
78%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
A particle moves in one dimension such that its position \(x\) (in metres) and time \(t\) (in seconds) are related by \( t =\alpha x^2+\beta x,\)
where \(\alpha\) and \(\beta\) are constants. What is the relation between its velocity \(v\) and acceleration \(a\)?
where \(\alpha\) and \(\beta\) are constants. What is the relation between its velocity \(v\) and acceleration \(a\)?
| 1. | \(a=\alpha v \) | 2. | \(a=-2\alpha v\) |
| 3. | \(a=-2\alpha v^3 \) | 4. | \(a=2\alpha v^2\) |
Subtopic: Acceleration |
64%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
A particle covers \(102.5~\text m\) in \(n^\text{th}\) second and \(115~\text m \) in \((n+2)^\text{th} \) second. Then the acceleration of the particle is:
1. \(\dfrac{25}{4}~\text{ms}^{-2} \)
2. \(\dfrac{27}{4}~\text{ms}^{-2} \)
3. \(\dfrac{34}{4}~\text{ms}^{-2} \)
4. \(\dfrac{39}{4}~\text{ms}^{-2} \)
1. \(\dfrac{25}{4}~\text{ms}^{-2} \)
2. \(\dfrac{27}{4}~\text{ms}^{-2} \)
3. \(\dfrac{34}{4}~\text{ms}^{-2} \)
4. \(\dfrac{39}{4}~\text{ms}^{-2} \)
Subtopic: Acceleration |
77%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
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 |
67%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
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%+
Please attempt this question first.
Hints
Please attempt this question first.
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%+
Please attempt this question first.
Hints
Please attempt this question first.
© 2026 GoodEd Technologies Pvt. Ltd.