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.
A particle moving along the x-axis has acceleration \(f,\) at time \(t,\) given by, \(f=f_0\left ( 1-\frac{t}{T} \right ),\) where \(f_0\) and \(T\) are constants. The particle at \(t=0\) has zero velocity. In the time interval between \(t=0\) and the instant when \(f=0,\) the particle’s velocity \( \left ( v_x \right )\) is:
1. \(f_0T\)
2. \(\frac{1}{2}f_0T^{2}\)
3. \(f_0T^2\)
4. \(\frac{1}{2}f_0T\)
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. \(26\)
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.
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. |