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/s² along the north. The velocity of the body just after \(4\) s will be?

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 one-fourth distance starting from the rest at the top? 

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 $30°$) is:

A particle starts from the origin at t = 0 sec with a velocity of $10$ $\hat{j}$ $m/s$ and moves in the x-y 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?

A particle starts from the origin at t = 0 with a velocity of 5.0î m/s and moves in the x-y 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 x-coordinate is 84 m?

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. $\frac{1}{\sin \theta }\sqrt{\frac{2h}{g}}$ 

4. $\sin \theta \sqrt{\frac{2h}{g}}$

A frictionless wire AB is fixed on a sphere of radius R. A very small spherical ball slips on this wire. The time taken by this ball to slip from A to B is:
          

1. $\frac{2\sqrt{gR}}{g\cos \theta }$

2. $2\sqrt{gR}.\frac{\cos \theta }{g}$

3. $2\sqrt{\frac{R}{g}}$ 

4. $\frac{gR}{\sqrt{g\cos \theta }}$