Referring to a-s diagram as shown in the figure. Find the velocity of the particle when the particle just covers 20 m $({\mathrm{v}}_0=\sqrt{50}\mathrm{m} {\mathrm{s}}^{-1})$.

1. $\sqrt{350}m s^{-1}$

2. $\sqrt{300}m s^{-1}$

3. $\sqrt{100}m s^{-1}$

4. $10m s^{-1}$

A point starts moving in a straight line with a certain acceleration. At a time 't' after beginning of motion the acceleration suddenly becomes retardation of the same value. The time in which the point returns to the initial point is-

1. $\sqrt{2\mathrm{t}}$

2. $\left(2+\sqrt{2}\right)\mathrm{t}$

3. $\frac{\mathrm{t}}{\sqrt{2}}$

4. Cannot be predicted unless acceleration is given

For acceleration of a particle varies with time as shown in the figure. Calculate the displacement of the particle in the time interval from t=2 s to t=4 s.

1. $\frac{20}{3}m$

2. 20 m

3. 10 m

4. $\frac{10}{3}m$

Two bodies, \(A\) (of mass \(1~\text{kg}\)) and \(B\) (of mass \(3~\text{kg}\)) are dropped from heights of \(16~\text{m}\) and \(25~\text{m}\), respectively. The ratio of the time taken by them to reach the ground is:
1. \(\frac{5}{4}\)
2. \(\frac{12}{5}\)
3. \(\frac{5}{12}\)
4. \(\frac{4}{5}\)

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. \(\frac{1}{2}f_0T\)

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:

The position of a particle with respect to time \(t\) along the \(\mathrm{x}\)-axis is given by \(x=9t^{2}-t^{3}\) where \(x\) is in metres and \(t\) in seconds. What will be the position of this particle when it achieves maximum speed along the \(+\mathrm{x} \text-\text{direction}?\)
1. \(32\) m
2. \(54\) m
3. \(81\) m
4. \(24\) m

A particle shows the distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point:

         

A particle starts its motion from rest under the action of a constant force. If the distance covered in the first \(10\) s is \(S_1\) and that covered in the first \(20\) s is \(S_2\), then:
1. \(S_2=2S_1\)
2. \(S_2 = 3S_1\)
3. \(S_2 = 4S_1\)
4. \(S_2= S_1\)