# A body starting from rest moves with uniform acceleration on a horizontal surface. The body covers $$3$$ consecutive equal distances from the beginning in time $$t_1, t_2,\text{and}~t_3$$${}_{}$ seconds. The ratio of $$t_1:t_2:t_3$$ is: 1. $$1:2:3$$ 2. $$1:\sqrt{2}:\sqrt{3}$$ 3. $$1:\left(\sqrt{2}-1\right):\left(\sqrt{3}-\sqrt{2}\right)$$ 4. $$\sqrt{3}:\sqrt{2}:1$$

Subtopic:  Uniformly Accelerated Motion |
80%
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The position ($$x$$) of a particle in a straight line motion is given by $$x = 2 + 10 t - 5 t^{2}~\text{m}$$. Its velocity ($$v$$) is best represented by?

 1 2 3 4
Subtopic:  Graphs |
76%
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An elevator whose floor to ceiling height is $$12$$ meters, moves upward with an acceleration of $$2.2~\text{m/s}^2$$. After $$1.5$$ seconds since starting, a bolt falls from its ceiling. The time taken by the bolt to reach the floor is:
1. $$1~\text{s}$$
2. $$2~\text{s}$$
3. $$\sqrt{2}~\text{s}$$
4. $$\sqrt{3}~\text{s}$$

Subtopic:  Relative Motion in One Dimension |
63%
From NCERT
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The displacement $$(x)$$ of a point moving in a straight line is given by; $$x=8t^2-4t.$$ Then the velocity of the particle is zero at:

 1 $$0.4$$ s 2 $$0.25$$ s 3 $$0.5$$ s 4 $$0.3$$ s
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
87%
From NCERT
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The velocity $$v$$ of an object varies with its position $$x$$ on a straight line as $$v=3\sqrt{x}.$$ Its acceleration versus time $$(a\text-t)$$ graph is best represented by:

 1 2 3 4
Subtopic:  Acceleration |
61%
From NCERT
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A particle is moving along the $$x$$-axis such that its velocity varies with time as per the equation $$v = 20\left(1-\frac{t}{2}\right)$$. At $$t=0$$ particle is at the origin. From the following, select the correct position $$(x)$$ - time $$(t)$$ plot for the particle:

 1 2 3 4
Subtopic:  Non Uniform Acceleration |
58%
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Suppose you are riding a bike with a speed of $$20$$ m/s due east relative to a person $$A$$ who is walking on the ground towards the east. If your friend $$B$$ walking on the ground due west measures your speed as $$30$$ m/s due east, find the relative velocity between two reference frames $$A$$ and $$B$$:

 1 The velocity of $$A$$ with respect to $$B$$ is $$5$$ m/s towards the east. 2 The velocity of $$A$$ with respect to $$B$$ is $$5$$ m/s towards the west. 3 The velocity of $$A$$ with respect to $$B$$ is $$10$$ m/s towards the east. 4 The velocity of $$A$$ with respect to $$B$$ is $$10$$ m/s towards the west.
Subtopic:  Relative Motion in One Dimension |
63%
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A ball is thrown vertically downwards with a velocity of $$20$$ m/s from the top of a tower. It hits the ground after some time with the velocity of $$80$$ m/s . The height of the tower is: (assuming $$g = 10~\text{m/s}^2)$$

 1 $$340$$ m 2 $$320$$ m 3 $$300$$ m 4 $$360$$ m
Subtopic:  Uniformly Accelerated Motion |
83%
From NCERT
NEET - 2020
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The position $$x$$ of a particle moving along the $$x$$-axis varies with time $$t$$ as $$x=20t-5t^2,$$
where $$x$$ is in meters and $$t$$ is in seconds. The particle reverses its direction of motion at:

1. $$x=40~\text{m}$$
2. $$x=10~\text{m}$$
3. $$x=20~\text{m}$$
4. $$x=30~\text{m}$$

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
81%
From NCERT
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A particle moves a distance $$x$$ in time $$t$$ according to equation $$x = (t+5)^{-1}$$. The acceleration of the particle is proportional to:

 1 $$(\text{velocity})^{\frac{3}{2}}$$ 2 $$(\text{distance})^2$$ 3 $$(\text{distance})^{-2}$$ 4 $$(\text{velocity})^{\frac{2}{3}}$$
Subtopic:  Acceleration |
66%
From NCERT
NEET - 2010
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