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.	\(2c, -2d\)

Acceleration-time graph of a body is shown.

 
The corresponding velocity-time graph of the same body is: 

1.		2.
3.		4.

A point moves in a straight line under the retardation \(av^2\)${\mathrm{}}^{}$. 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. \(a~\mathrm{ln}(aut)\)

The acceleration \(a\) (in ${\mathrm{ms}}^{-2}$) 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:

A particle moves a distance \(x\) in time \(t\) according to equation \(x=(t+5)^{-1}.\) The acceleration of the particle is proportional to:
1. (velocity)^\(3/2\)
2. (distance)^\(2\)
3. (distance)^\(-2\)
4. (velocity)^\(2/3\)

The distance travelled by a particle starting from rest and moving with an acceleration \(\frac{4}{3}\) ms^-2, in the third second is:
1. \(6\) m
2. \(4\) m
3. \(\frac{10}{3}\) m
4. \(\frac{19}{3}\) m

A car moves from \(X\) to \(Y\) with a uniform speed \(v_u\) and returns to \(X\) with a uniform speed \(v_d.\) The average speed for this round trip is:

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 graph of displacement time is given below.

Its corresponding velocity-time graph will be:

1.		2.
3.		4.