- 1(current)
Q. No.The displacement of a particle is given by \(y = a + bt + ct^{2} - dt^{4}\). The initial velocity and acceleration are, respectively:
| 1. | \(b, -4d\) | 2. | \(-b,2c\) |
| 3. | \(b, ~2c\) | 4. | \(2c, -2d\) |
The motion of a particle along a straight line is described by the equation; \(x=8+12 t-t^3,\) where \(x\) is in metre and \(t\) is in second. The retardation of the particle when its velocity becomes zero is:
| 1. | \(24 ~\text{ms}^{-2} \) | 2. | zero |
| 3. | \( 6 ~\text{ms}^{-2} \) | 4. | \(12 ~\text{ms}^{-2} \) |
The acceleration \(a\) (in ) of a body, starting from rest varies with time \(t\) (in \(\mathrm{s}\)) as per the equation \(a=3t+4.\) The velocity of the body at time \(t=2\) \(\mathrm{s}\) will be:
| 1. | \(10~\text{ms}^{-1}\) | 2. | \(18~\text{ms}^{-1}\) |
| 3. | \(14~\text{ms}^{-1}\) | 4. | \(26~\text{ms}^{-1}\) |
| 1. | \(- 2 nβ^{2} x^{- 2 n - 1}\) | 2. | \(- 2 nβ^{2} x^{- 4 n - 1}\) |
| 3. | \(- 2 \beta^{2} x^{- 2 n + 1}\) | 4. | \(- 2 nβ^{2} x^{- 4 n + 1}\) |
| 1. | \(-\frac{1}{2}\left(a\omega^2\sin\omega t\right)t^2\) | 2. | \(a\omega \sin \omega t\) |
| 3. | \(a\omega \cos \omega t\) | 4. | \(a\sin \omega t\) |
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. |  |
A particle is moving along the \(x\)-axis such that its velocity varies with time as per the equation \(v = 20\left(1-\frac{t}{2}\right)\). At \(t=0\) particle is at the origin. From the following, select the correct position \((x)\) - time \((t)\) plot for the particle:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
A point moves in a straight line under the retardation \(av^2\). If the initial velocity is \(u,\) the distance covered in \(t\) seconds is:
1. \((aut)\)
2. \(\frac{1}{a}\mathrm{ln}(aut)\)
3. \(\frac{1}{a}\mathrm{ln}(1+aut)\)
4. \(a~\mathrm{ln}(aut)\)
A body is thrown vertically upwards. If the air resistance is to be taken into account, then the time during which the body rises is:
| 1. | Equal to the time of fall. |
| 2. | Less than the time of fall. |
| 3. | Greater than the time of fall. |
| 4. | Twice the time of fall. |
The initial velocity of a particle is \(u\) (at \(t=0\)) and the acceleration \(f\) is given by \(at\). Which of the following relation is valid?
1. \(v = u + a t^{2}\)
2. \(v = u + a \frac{t^{2}}{2}\)
3. \(v = u + a t\)
4. \(v= u\)
- 1(current)
Q. No.
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