A particle has an initial velocity (\(2\mathrm{i}+3\mathrm{j}\)) and an acceleration (\(0.3\mathrm{i}+0.2\mathrm{j}\)). The magnitude of velocity after 10 s will be:
1. \(9 \sqrt{2} ~\text{units} \)
2. \(5 \sqrt{2} ~\text{units} \)
3. \(5 ~\text{units} \)
4. \(9~\text{units} \)
A particle has an initial velocity $\overrightarrow{\mathrm{u}}=(4\hat{i}5\hat{j})$ m/s and it is moving with an acceleration $\overrightarrow{\mathrm{a}}=\left(\frac{1}{4}\hat{i}+\frac{1}{5}\hat{j}\right)m/{s}^{2}$. Velocity of the particle at \(t=2\) s will be:
1. $(6\hat{\mathrm{i}}4\hat{\mathrm{j}})\mathrm{m}/\mathrm{s}$
2. $(4.5\hat{i}4.5\hat{\mathrm{j}})\mathrm{m}/\mathrm{s}$
3. $(4.5\hat{i}4.6\hat{\mathrm{j}})\mathrm{m}/\mathrm{s}$
4. $(6\hat{\mathrm{i}}4.6\hat{\mathrm{j}})\mathrm{m}/\mathrm{s}$
A body started moving with an initial velocity of \(4\) m/s along the east and an acceleration \(1\) m/s^{2} along the north. The velocity of the body just after \(4\) s will be?
1.  \(8\) m/s along East 
2.  \(4 \sqrt{2} \) m/s along NorthEast 
3.  \(8\) m/s along North 
4.  \(4 \sqrt{2} \) m/s along SouthEast 
A body sliding on a smooth inclined plane requires 4 seconds to reach the bottom starting from the rest at the top. How much time does it take to cover onefourth distance starting from the rest at the top?
1.  1 s  2.  2 s 
3.  4 s  4.  16 s 
The time taken by a block of wood (initially at rest) to slide down a smooth inclined plane 9.8 m long (angle of inclination is $30\xb0$) is:
1.  \(\frac{1}{2} \mathrm{sec} \)  2.  \(2 ~\mathrm{sec} \) 
3.  \(4~ \mathrm{sec} \)  4.  \(1~ \mathrm{sec} \) 
A particle starts from the origin at t = 0 with a velocity of 5.0î m/s and moves in the xy plane under the action of a force that produces a constant acceleration of (3.0î +2.0 ĵ ) $\mathrm{m}/{\mathrm{s}}^{2}$. What is the speed of the particle at the instant its xcoordinate is 84 m?
1.  36 m/s  2.  26 m/s 
3.  1 m/s  4.  0 m/s 
A particle starts from the origin at t = 0 sec with a velocity of $10$ $\hat{j}$ $m/s$ and moves in the xy plane with a constant acceleration of \((8.0\hat i +2.0 \hat j)\) \(\text{ms}^{2}\). At what time is the x coordinate of the particle 16 m?
1.  2 s

2.  3 s

3.  4 s

4.  1 s 
A particle starts moving with constant acceleration with initial velocity (\(\hat{\mathrm{i}}+5\hat{\mathrm{j}}\)$\stackrel{}{\mathrm{}}$) m/s. After \(4\) seconds, its velocity becomes (\(3\hat{\mathrm{i}}2\hat{\mathrm{j}}\)) m/s. The magnitude of its displacement in 4 seconds is:
1. \(5\) m
2. \(10\) m
3. \(15\) m
4. \(20\) m
A body is slipping from an inclined plane of height h and length l. If the angle of inclination is θ, the time taken by the body to come from the top to the bottom of this inclined plane is:
1. $\sqrt{\frac{2h}{g}}$
2. $\sqrt{\frac{2l}{g}}$
3. $\frac{1}{\mathrm{sin}\theta}\sqrt{\frac{2h}{g}}$
4. $\mathrm{sin}\theta \sqrt{\frac{2h}{g}}$
A particle starts from the origin at t = 0 with a velocity of 5.0î m/s and moves in the xy plane under the action of a force that produces a constant acceleration of (3.0î +2.0ĵ ) $m/{s}^{2}$. What is the ycoordinate of the particle at the instant its xcoordinate is 84 m?
1. 36 m
2. 26 m
3. 1 m
4. 0 m