The displacement of a particle is given by . The initial velocity and acceleration are, respectively:
1. | \(\mathrm{b}, ~\mathrm{-4d}\) | 2. | \(\mathrm{-b},~ \mathrm{2c}\) |
3. | \(\mathrm{b}, ~\mathrm{2c}\) | 4. | \(\mathrm{2c}, ~\mathrm{-2d}\) |
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. \(10\)
2. \(18\)
3. \(14\)
4. \(26\)
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. | \(12 ~\text{ms}^{-2} \) |
A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to where and \(\mathrm{n}\) are constants and \(\mathrm{x}\) is the position of the particle. The acceleration of the particle as a function of \(\mathrm{x}\) is given by:
1.
2.
3.
4.
The acceleration of a particle starting from rest varies with time according to the relation A = – aω2sinωt. The displacement of this particle at a time t 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 . 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. |
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 point moves in a straight line under the retardation a. If the initial velocity is \(\mathrm{u},\) the distance covered in \(\mathrm{t}\) seconds is:
1.
2.
3.
4.
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.
2.
3.
4. v = u