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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Rain is falling vertically with a speed of $$35$$ m/s. A woman rides a bicycle with a speed of $$12$$ m/s in the east-to-west direction. What is the direction in which she should hold her umbrella?

 1 in the vertical direction only. 2 $$19^\circ$$ with vertical towards east. 3 $$19^\circ$$ with vertical towards the west. 4 $$19^\circ$$ with vertical towards the south.
Subtopic: Â Relative Motion |
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Galileo, in his book Two new sciences, stated that for elevations that exceed or fall short of $$45^\circ$$ by equal amounts, the ranges:

 1 are equal to each other. 2 are not equal to each other. 3 are sometimes equal and sometimes not equal to each other. 4 depends on the difference between the angles.

Subtopic: Â Projectile Motion |
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A hiker stands on the edge of a cliff $$490~\mathrm{m}$$ above the ground and throws a stone horizontally with an initial speed of $$15$$ m/s. Neglecting air resistance, the time taken by the stone to reach the ground and the speed with which it hits the ground are, respectively: (Take $$g=9.8~\mathrm{m/s^2}$$)

 1 $$10$$ s and $$99$$ m/s 2 $$10$$ s and $$15$$ m/s 3 $$5$$ s and $$99$$ m/s 4 $$5$$ s and $$15$$ m/s

Subtopic: Â Projectile Motion |
Â 71%
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A cricket ball is thrown at a speed of $$28$$ m/s in a direction $$30^\circ$$ above the horizontal. The time taken by the ball to return to the same level is:
1. $$2.5$$ s
2. $$2.9$$ s
3. $$3.5$$ s
4. $$3$$ s

Subtopic: Â Projectile Motion |
Â 85%
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An insect trapped in a circular groove of radius $$12$$ cm moves along the groove steadily and completes $$7$$ revolutions in $$100$$ s. What is the angular speed of the motion?

 1 $$0.62$$ rad/s 2 $$0.06$$ rad/s 3 $$4.40$$ rad/s 4 $$0.44$$ rad/s
Subtopic: Â Circular Motion |
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An insect trapped in a circular groove of radius $$12$$ cm moves along the groove steadily and completes $$7$$ revolutions in $$100$$ s. Is the acceleration vector a constant vector? What is its magnitude?
1. $$\text{yes},$$ $$2.3~\text{cm/s}^2$$
2. $$\text{no},$$ $$5.3~\text{cm/s}^2$$
3. $$\text{yes},$$ $$5.3~\text{cm/s}^2$$
4. $$\text{no},$$ $$2.3~\text{cm/s}^2$$

Subtopic: Â Circular Motion |
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A cricket ball is thrown at a speed of $$28$$ m/s in a direction $$30^{\circ}$$ above the horizontal. The maximum height attained by the ball is:
1. $$5$$ m
2. $$10$$ m
3. $$15$$ m
4. $$20$$ m

Subtopic: Â Projectile Motion |
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The position of a particle is given by;
$$\vec{r}=(3.0t\hat{i}-2.0t^{2}\hat{j}+4.0\hat{k})$$ m where $$t$$ is in seconds and the coefficients have the proper units for $$r$$ to be in metres. The magnitude and direction of $$\vec{v}(t)$$ at$$t=1.0$$ s are:
1. $$4$$m/s,$$53^\circ$$ with $$x$$-axis
2. $$4$$ m/s, $$37^\circ$$ with $$x$$-axis
3. $$5$$ m/s,$$53^\circ$$ with $$y$$-axis
4. $$5$$m/s, $$53^\circ$$ with $$x$$-axis
Subtopic: Â Speed & Velocity |
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A motorboat is racing towards the north at $$25$$ km/h and the water current in that region is $$10$$ km/h in the direction of $$60^\circ$$ east of the south. The resultant velocity of the boat is:

 1 $$12$$ km/h at $$23 . 4^\circ$$ east of west 2 $$22$$ km/h at $$23 . 4^\circ$$ north of east 3 $$22$$ km/h at $$23 . 4^\circ$$ east of north 4 $$20$$ km/h at $$23 . 4^\circ$$ north of west

Subtopic: Â Relative Motion |
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