A particle has an initial velocity ($$2\hat{i}+3\hat{j}$$) and an acceleration ($$0.3\hat{i}+0.2\hat{j}$$). 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. $$9~\text{units}$$

Subtopic: Â Uniformly Accelerated Motion |
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A particle has an initial velocity $$\overrightarrow{u} = \left(4 \hat{i} - 5 \hat{j}\right)$$ m/s and it is moving with an acceleration $$\overrightarrow{a} = \left(\frac{1}{4} \hat{i} + \frac{1}{5} \hat{j}\right)\text{m/s}^{2}$$. Velocity of the particle at $$t=2$$ s will be:
1. $$(6\hat i -4\hat j)~\text{m/s}$$
2. $$(4.5\hat i -4.5\hat j)~\text{m/s}$$
3. $$(4.5\hat i -4.6\hat j)~\text{m/s}$$
4. $$(6\hat i -4.6\hat j)~\text{m/s}$$

Subtopic: Â Uniformly Accelerated Motion |
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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?

 1 $$8$$ m/s along East. 2 $$4 \sqrt{2}$$ m/s along North-East. 3 $$8$$ m/s along North. 4 $$4 \sqrt{2}$$ m/s along South-East.
Subtopic: Â Uniformly Accelerated Motion |
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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?

 1 $$1~\text{s}$$ 2 $$2~\text{s}$$ 3 $$4~\text{s}$$ 4 $$16~\text{s}$$
Subtopic: Â Uniformly Accelerated Motion |
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The time taken by a block of wood (initially at rest) to slide down a smooth inclined plane $$9.8~\text{m}$$ long (angle of inclination is $$30^{\circ}$$) is:

 1 $$\frac{1}{2}~\text{sec}$$ 2 $$2 ~\text{sec}$$ 3 $$4~ \text{sec}$$ 4 $$1~\text{sec}$$
Subtopic: Â Uniformly Accelerated Motion |
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A particle starts from the origin at $$t=0$$ sec with a velocity of $$10\hat j~\text{m/s}$$ and moves in the $$x\text-y$$ plane with a constant acceleration of $$(8.0\hat i +2.0 \hat j)~\text{m/s}^2$$. At what time is the $$x\text-$$coordinate of the particle $$16$$ m?
1. $$2$$ s

2. $$3$$ s

3. $$4$$ s

4. $$1$$ s

Subtopic: Â Uniformly Accelerated Motion |
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A particle starts from the origin at $$t=0$$ with a velocity of $$5.0\hat i$$ m/s and moves in the $$x\text-y$$ plane under the action of a force that produces a constant acceleration of $$(3.0\hat i + 2.0\hat j)~\text{m/s}^2$$. What is the speed of the particle at the instant its $$x\text-$$coordinate is $$84$$ m?

1. $$36$$ m/s
2. $$26$$ m/s
3. $$1$$ m/s
4. $$0$$ m/s
Subtopic: Â Uniformly Accelerated Motion |
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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

Subtopic: Â Uniformly Accelerated Motion |
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A body is slipping from an inclined plane of height $$h$$ and length $$l$$. If the angle of inclination is $$\theta$$, the time taken by the body to come from the top to the bottom of this inclined plane is:
1. $$\sqrt{\frac{2 h}{g}}$$
2. $$\sqrt{\frac{2 l}{g}}$$
3. $$\frac{1}{\sin \theta} \sqrt{\frac{2 h}{g}}$$
4. $$\sin \theta \sqrt{\frac{2 h}{g}}$$

Subtopic: Â Uniformly Accelerated Motion |
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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. $$\frac{2 \sqrt{g R}}{g \cos \theta}$$
2. $$2 \sqrt{g R} . \frac{\cos \theta}{g}$$
3. $$2 \sqrt{\frac{R}{g}}$$
4. $$\frac{g R}{\sqrt{g\cos \theta}}$$

Subtopic: Â Uniformly Accelerated Motion |
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