The x and y coordinates of the particle at any time are x=5t-2$t^2$ and y=10t respectively, where x and y are in the metres and t is in seconds. The acceleration of the particle at t=2s is :

1. 0

2. 5$m/s^2$

3. -4$m/s^2$

4. -8 $m/s^2$

A particle is moving such that its position coordinates \((x,y)\) are \(​ (2~\text m,  3~\text m)​\) at time \(t=0,\)   \(​ (6~\text m,  7~\text m)​\) at time \(t=2~\text s\)  and \(​ (13~\text m,  14~\text m)​\) at time \(t=5~\text s.\)  The average velocity vector \((v_{avg})\) from \(t=0\) to \(t=5~\text s\) is:

A body is moving with velocity 30 m/s towards east. After 10 s its velocity becomes 40 m/s towards north. The average acceleration of the body is

(1) $7 \mathrm{m}/{\mathrm{s}}^2$                                             

(2) $\sqrt{7} \mathrm{m}/{\mathrm{s}}^2$

(3) $5 \mathrm{m}/{\mathrm{s}}^2$                                             

(4) $1 \mathrm{m}/{\mathrm{s}}^2$

A missile is fired for maximum range with an initial velocity of 20 m/s. If g=10 $\mathrm{m}/{\mathrm{s}}^2$, the range of the missile is

1. 50 m                                                          2. 60 m

3. 20 m                                                          4. 40 m

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. $45°$

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

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 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 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:

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. \(\frac{\pi}{2}\)