A stone is just released from the window of a train moving along a horizontal straight track. The stone will hit the ground following

(1) Straight path

(2) Circular path

(3) Parabolic path

(4) Hyperbolic path

What determines the nature of the path followed by a particle:
1. Speed
2. Velocity
3. Acceleration
4. Both (2) and (3)

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

1.  4m

2.  $\sqrt{20}\mathrm{m}$

3.  $>\sqrt{20}\mathrm{m}$

4.  $<\sqrt{20}\mathrm{m}$

Two particles are projected simultaneously from the level ground as shown in figure. They may collide after a time :

1. $\frac{{\mathrm{xsin\theta }}_2}{{\mathrm{u}}_1}$

2. $\frac{{\mathrm{xcos\theta }}_2}{{\mathrm{u}}_1}$

3. $\frac{{\mathrm{xsin\theta }}_2}{{\mathrm{u}}_1\sin \left({\mathrm{\theta }}_2-{\mathrm{\theta }}_1\right)}$

4. $\frac{{\mathrm{xsin\theta }}_1}{{\mathrm{u}}_2\sin \left({\mathrm{\theta }}_2-{\mathrm{\theta }}_1\right)}$

If \(\overrightarrow {A}= \overrightarrow{B}+ \overrightarrow{C}\) and the magnitudes of \(\overrightarrow {A}, \overrightarrow {B},\overrightarrow {C}\) are \(5,4\) and \(3\) units, respectively. Then the angle between \(\overrightarrow {A}~\text{and}~\overrightarrow{C}\)$\stackrel{}{}$is:
1. \(\cos^{-1}\left(\frac{3}{5}\right)\)
2. \(\cos^{-1}\left(\frac{4}{5}\right)\)
3. \(\sin^{-1}\left(\frac{3}{4}\right)\)
4. \(\frac{\pi}{2}\)

The coordinates of a moving particle at a time \(t\), are given by, \(x= 5\sin 10t, y = 5\cos 10t\). It can be deduced that the speed of the particle will be:

A particle moves in space such that

$\mathrm{x}=2{\mathrm{t}}^3+3\mathrm{t}+4 ; \mathrm{y}={\mathrm{t}}^2+4\mathrm{t}-1 ; \mathrm{z}=2 \sin \mathrm{\pi t}$

Where x, y, z are measured in metre and t in second. The acceleration of the particle at t=3s is

(A)  $36\hat{\mathrm{i}}+2\hat{\mathrm{j}}+\hat{\mathrm{k}} {\mathrm{ms}}^{-2}$

(B)  $36\hat{\mathrm{i}}+2\hat{\mathrm{j}}+\mathrm{\pi }\hat{\mathrm{k}} {\mathrm{ms}}^{-2}$

(C)  $36\hat{\mathrm{i}}+2\hat{\mathrm{j}} {\mathrm{ms}}^{-2}$

(D)  $12\hat{\mathrm{i}}+2\hat{\mathrm{j}} {\mathrm{ms}}^{-2}$

The speed of a projectile at its maximum height is half of its initial speed. The angle of projection is:

1. $60°$                                         2. $15°$

3. $30°$                                          4. $45°$

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

(1) 7unit                                                         

(2) 7$\sqrt{2}$unit

(3) 8.5 unit                                                     

(4) 10 unit

A projectile is fired at an angle of 45$°$ with the horizontal. The elevation angle of the projectile at its highest point as seen from the point of projection is:

1. 60$°$                                           2. ${\tan }^{-1}\left(\frac{1}{2}\right)$

3. ${\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)$                               4. $45°$