# A cat is situated at point $$A$$ ($$0,3,4$$) and a rat is situated at point $$B$$ ($$5,3,-8$$). The cat is free to move but the rat is always at rest. The minimum distance travelled by the cat to catch the rat is: 1. $$5$$ unit 2. $$12$$ unit 3. $$13$$ unit 4. $$17$$ unit

Subtopic:  Position & Displacement |
75%
From NCERT
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The position of a moving particle at time $$t$$ is $$\overrightarrow{r}=3\hat{i}+4t^{2}\hat{j}-t^{3}\hat{k}.$$ Its displacement during the time interval $$t=1$$ s to $$t=3$$ s will be:

 1 $$\hat{j}-\hat{k}$$ 2 $$3\hat{i}-4\hat{j}-\hat{k}$$ 3 $$9\hat{i}+36\hat{j}-27\hat{k}$$ 4 $$32\hat{j}-26\hat{k}$$
Subtopic:  Position & Displacement |
81%
From NCERT
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Which of the following statements is incorrect?

 1 The average speed of a particle in a given time interval cannot be less than the magnitude of the average velocity. 2 It is possible to have a situation $$\left|\frac{d\overrightarrow {v}}{dt}\right|\neq0$$ but $$\frac{d\left|\overrightarrow{v}\right|}{dt}=0$$ 3 The average velocity of a particle is zero in a time interval. It is possible that instantaneous velocity is never zero in that interval. 4 It is possible to have a situation in which $$\left|\frac{d\overrightarrow{v}}{dt}\right|=0$$ but $$\frac{d\left|\overrightarrow{v}\right|}{dt}\neq0$$
Subtopic:  Acceleration |
63%
From NCERT
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A particle is moving along a curve. Select the correct statement.

 1 If its speed is constant, then it has no acceleration. 2 If its speed is increasing, then the acceleration of the particle is along its direction of motion. 3 If its speed is decreasing, then the acceleration of the particle is opposite to its direction of motion. 4 If its speed is constant, its acceleration is perpendicular to its velocity.
Subtopic:  Acceleration |
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A particle is moving on a circular path of radius $$R.$$ When the particle moves from point $$A$$ to $$B$$ (angle $$\theta$$), the ratio of the distance to that of the magnitude of the displacement will be:

 1 $\frac{\mathrm{\theta }}{\mathrm{sin}\frac{\mathrm{\theta }}{2}}$ 2 $\frac{\mathrm{\theta }}{2\mathrm{sin}\frac{\mathrm{\theta }}{2}}$ 3 $\frac{\mathrm{\theta }}{2\mathrm{cos}\frac{\mathrm{\theta }}{2}}$ 4 $\frac{\mathrm{\theta }}{\mathrm{cos}\frac{\mathrm{\theta }}{2}}$ 
Subtopic:  Position & Displacement |
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From NCERT
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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:  Uniformly Accelerated Motion |
78%
From NCERT
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If three coordinates of a particle change according to the equations $$x = 3 t^{2}, y = 2 t , z= 4$$, then the magnitude of the velocity of the particle at time $$t=1$$ second will be:
1. $$2\sqrt{11}~\text{unit}$$
2. $$\sqrt{34}~\text{unit}$$

3. $$40~\text{unit}$$
4. $$2\sqrt{10}~\text{unit}$$

Subtopic:  Speed & Velocity |
81%
From NCERT
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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:  Uniformly Accelerated Motion |
65%
From NCERT
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Three girls skating on a circular ice ground of radius $$200$$ m start from a point $$P$$ on the edge of the ground and reach a point $$Q$$ diametrically opposite to $$P$$ following different paths as shown in the figure. The correct relationship among the magnitude of the displacement vector for three girls will be:

1. $$A > B > C$$
2. $$C > A > B$$
3. $$B > A > C$$
4. $$A = B = C$$

Subtopic:  Position & Displacement |
84%
From NCERT
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A particle is moving such that its position coordinates $$(x,y)$$ are $$(2$$ m, $$3$$ m) at time $$t=0,$$ $$(6$$ m, $$7$$ m) at time $$t=2$$ s and $$(13$$ m, $$14$$ m) at time $$t=5$$ s. Average velocity vector $$(v_{avg})$$ from $$t=0$$ to $$t=5$$ s is:

 1 $$\frac{1}{5}\left ( 13\hat{i}+14\hat{j} \right )$$ 2 $$\frac{7}{3}\left ( \hat{i}+\hat{j} \right )$$ 3 $$2\left ( \hat{i}+\hat{j} \right )$$ 4 $$\frac{11}{5}\left ( \hat{i}+\hat{j} \right )$$
Subtopic:  Speed & Velocity |
82%
From NCERT
NEET - 2014
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