A man weighing 80 kg is standing in a trolley weighing 320 kg. The trolley is resting on frictionless horizontal rails. If the man starts walking on the trolley with a speed of 1 m/s, then after 4 sec his displacement relative to the ground will be

1. 5  m

2. 4.8 m

3. 3.2 m

4. 3.0 m

A particle is projected at an angle \(𝜃  \) with the horizontal with an initial speed \(u\). When it makes an angle \(𝛼\) with the horizontal, its speed \(v\) is:
1. \(𝑢 \cos 𝜃\)

2. \(𝑢 \cos 𝜃 \ 𝑢 \cos 𝛼 \)

3. \(\dfrac{u\sin \theta}{\sin \alpha}\)

4. \(\dfrac{u\cos \theta}{\cos \alpha}\)

A particle is moving along the path y = ${\mathrm{x}}^2$ from x = 0 m to x = 2 m. Then the distance traveled by the particle is:

1.  4 m

2.  $\sqrt{20}<mspace\; width="1em"></mspace>\mathrm{m}$

3.  $>\sqrt{20}<mspace\; width="1em"></mspace>\mathrm{m}$

4.  $<\sqrt{20}<mspace\; width="1em"></mspace>\mathrm{m}$

A body is projected with velocity \(20\sqrt3 \text{  m/s}\) with an angle of projection \(60^°\) with the horizontal. The velocity at the point where the body makes an angle \(30^°  \)with the horizontal is:

1. \(20 \text{  m/s}\)

2. \(\dfrac{20}{\sqrt3} \text{  m/s}\)

3. \(10\sqrt3 \text{  m/s}\)

4. \(10 \text{  m/s}\)

In a uniform circular motion, which of the following quantity is not constant

1. Angular momentum

2. Speed

3. Kinetic energy

4. Momentum

A particle projected with kinetic energy ${\mathrm{k}}_0$ with an angle of projection $\mathrm{\theta }$. Then the variation of kinetic K with vertical displacement y is

1.  linear

2.  parabolic

3.  hyperbolic

4.  periodic

A body is projected with a velocity \(u\) with an angle of projection \(\theta.\) The change in velocity after the time \((t)\) from the time of projection will be:

A particle has initial velocity $\left(3\hat{\mathrm{i}}+4\hat{\mathrm{j}}\right)$ and has acceleration $\left(0.4\hat{\mathrm{i}}+0.3\hat{\mathrm{j}}\right)$. Its speed after 10 s:

1. 7 units

2. $7\sqrt{2}$ units

3. 8.5 units

4. 10 units

The gravity in space is given by \(\vec g=-10 \hat j\ \text{m/s}^{2}\). Two particles are simultaneously projected with velocity \(\vec u_1=10\ \text{m/s} \hat i+10\ \text{m/s} \hat j\) and \(\vec u_2=20\ \text{m/s} \hat i+10\ \text{m/s} \hat j\). Then, the ratio of their times of flight is:

1. \(1:1\)

2. \(1:2\)

3. \(2:1\)

4. None of the above

What determines the nature of the path followed by the particle?

1. Speed only

2. Velocity only

3. Acceleration only

4. None of these