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 $\theta$ with horizontal with an initital speed u. When it makes an angle $\alpha$ with horizontal, its speed v is-

1. $u\cos \theta$

2. $u\cos \theta <mspace\; width="1em"></mspace>u\cos \alpha$

3. $\frac{u\sin \theta }{\sin \alpha }$

4. $\frac{u\cos \theta }{\cos \alpha }$

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 $20\sqrt{3}$ m/s with an angle of projection 60$°$ with horizontal. Calculate velocity on that point where body makes an angle 30$°$ with the horizontal.

1. 20 m/s

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

3. $10\sqrt{3}<mspace\; width="1em"></mspace>m/s$

4. 10 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 $\overrightarrow{\mathrm{g}}=-10<mspace\; width="1em"></mspace>\hat{j}<mspace\; width="1em"></mspace>m{s}^{-2}$. Two particles are simultaneously projected with velocity $\overrightarrow{{\mathrm{u}}_1}=\left(10<mspace\; width="1em"></mspace>m{s}^{-1}\right)\hat{i}+\left(10<mspace\; width="1em"></mspace>m{s}^{-1}\right)\hat{j}$ and $\overrightarrow{{\mathrm{u}}_2}=\left(20<mspace\; width="1em"></mspace>m{s}^{-1}\right)\hat{i}+\left(10<mspace\; width="1em"></mspace>m{s}^{-1}\right)\hat{j}$. Then, the ratio of their times of flight

1. 1:1

2. 1:2

3. 2:1

4. none

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

1. Speed only

2. Velocity only

3. Acceleration only

4. None of these