A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude \(P_0\). The instantaneous velocity of this car is proportional to:
1.  \(t^{\frac{1}{2}}\)
2.  \(t^{\frac{-1}{2}}\)
3. \(\frac{t}{\sqrt{m}}\)
4. \(t^2 P_0\)

A stone is dropped from a height \(h\). It hits the ground with a certain momentum \(p\). If the same stone is dropped from a height \(100\)% more than the previous height, the momentum when it hits the ground will change by:
1. \(41\)% 
2. \(200\)% 
3. \(100\)% 
4. \(68\)%

A particle of mass \(M\) starting from rest undergoes uniform acceleration. If the speed acquired in time \(T\) is \(V\), the power delivered to the particle is:
1. \(\frac{1}{2}\frac{MV^2}{T^2}\)
2. \(\frac{MV^2}{T^2}\)
3. \(\frac{1}{2}\frac{MV^2}{T}\)
4. \(\frac{MV^2}{T}\)

A mass \(m\) moving horizontally (along the x-axis) with velocity \(v\) collides and sticks to a mass of \(3m\) moving vertically upward (along the y-axis) with velocity \(2v.\) The final velocity of the combination is:
1. \(\frac{3}{2}v\hat{i}+\frac{1}{4}v\hat{j}\)
2. \(\frac{1}{4}v\hat{i}+\frac{3}{2}v\hat{j}\)
3. \(\frac{1}{3}v\hat{i}+\frac{2}{3}v\hat{j}\)
4. \(\frac{2}{3}v\hat{i}+\frac{1}{3}v\hat{j}\)

If $x$ $=$ $3$ $-4t^2$ $+$ $t^3$, then work done in the first 4s will be:
(Mass of the particle is 3 gram)
1.  384 mJ
2.  168 mJ
3.  192 mJ
4.  None of the above

Two identical balls A and B are moving with velocity $+0.5$ $m{s}^{-1}$ and $-0.3$ $m{s}^{-1}$ respectively. If they collide head on elastically, then their velocities after collision will be:

1. $-0.3$ $m{s}^{-1}$ $and$ $0.5$ $m{s}^{-1}$

2. $+0.5$ $m{s}^{-1}$ $and$ $+$ $0.3$ $m{s}^{-1}$

3. $-0.4$ $m{s}^{-1}$ $and$ $0.3$ $m{s}^{-1}$

4. $-0.3$ $m{s}^{-1}$ $and$ $-0.4$ $m{s}^{-1}$

A bomb of mass 30kg at rest explodes into two pieces of masses 18 kg and 12 kg. The velocity of 18kg mass is 6ms^–1. The kinetic energy of the other mass is:

1. 524 J

2. 256 J

3. 486 J

4. 324 J

The bob of a simple pendulum having length l, is displaced from the mean position to an angular position θ with respect to vertical. If it is released, then the velocity of the bob at the lowest position will be:

1. $\sqrt{2gl(1-\cos \theta )}$

2. $\sqrt{2gl(1+\cos }$ $\theta )$

3. $\sqrt{2gl}$ $\cos \theta$

4. $\sqrt{2gl}$

If \(\vec{F} = (60\hat{i} + 15\hat{j}-3\hat{k})\) N and \(\vec{v} = (2\hat{i} - 4\hat{j}+5\hat{k})\) m/s, then instantaneous power is:
1. \(195\) watt
2. \(45\) watt
3. \(75\) watt
4. \(100\) watt

A ball is dropped from a height of \(5\) m. If it rebounds up to a height of \(1.8\) m, then the ratio of velocities of the ball after and before the rebound will be:
1. $\frac{3}{5}$

2. $\frac{2}{5}$

3. $\frac{1}{5}$

4. $\frac{4}{5}$