A particle is dropped vertically from rest from a height. The time taken by it to fall through successive distances of 1 m each will then be

(1) All equal, being equal to $\sqrt{2/g}$ second

(2) In the ratio of the square roots of the integers 1, 2, 3.....

(3) In the ratio of the difference in the square roots of the integers i.e. $\sqrt{1},\text{\hspace{0.17em}}\left(\sqrt{2}-\sqrt{1}\right),\text{\hspace{0.17em}}\left(\sqrt{3}-\sqrt{2}\right),\text{\hspace{0.17em}}\left(\sqrt{4}-\sqrt{3}\right)$ ....

(4) In the ratio of the reciprocal of the square roots of the integers i.e.,. $\frac{1}{\sqrt{1}},\text{\hspace{0.17em}}\frac{1}{\sqrt{2}},\frac{1}{\sqrt{3}},\text{\hspace{0.17em}}\frac{1}{\sqrt{4}}$

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A man throws balls with the same speed vertically upwards one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time (Given $g=9.8m/{s}^{2}\right)$

(1) At least 0.8 m/s

(2) Any speed less than 19.6 m/s

(3) Only with speed 19.6 m/s

(4) More than 19.6 m/s

Concept Questions :-

Acceleration
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If a ball is thrown vertically upwards with speed u, the distance covered during the last t seconds of its ascent is

(1) $\frac{1}{2}g{t}^{2}$

(2) $ut-\frac{1}{2}g{t}^{2}$

(3) $\left(u-gt\right)t$

(4) $ut$

Concept Questions :-

Uniformly accelerated motion
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The variation of velocity of a particle with time moving along a straight line is illustrated in the following figure. The distance travelled by the particle in four seconds is

1. 60 m

2. 55 m

3. 25 m

4. 30 m

Concept Questions :-

Graphs
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The displacement of a particle as a function of time is shown in the figure. The figure shows that

1. The particle starts with certain velocity but the motion is retarded and finally the particle stops

2. The velocity of the particle is constant throughout

3. The acceleration of the particle is constant throughout.

4. The particle starts with constant velocity, then motion is accelerated and finally the particle moves with another constant velocity

Concept Questions :-

Graphs
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A ball is thrown vertically upwards. Which of the following graph/graphs represent velocity-time graph of the ball during its flight (air resistance is neglected)

1. a

2. b

3. c

4. d

Concept Questions :-

Uniformly accelerated motion
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The graph between the displacement x and time t for a particle moving in a straight line is shown in figure. During the interval $OA,\text{\hspace{0.17em}}AB,\text{\hspace{0.17em}}BC$ and CD, the acceleration of the particle is

 OA AB BC CD (1) + 0 + + (2) – 0 + 0 (3) + 0 – + (4) – 0 – 0

Concept Questions :-

Graphs
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The vt graph of a moving object is given in figure. The maximum acceleration is

1. $1cm/se{c}^{2}$

2. $2cm/se{c}^{2}$

3. $3\text{\hspace{0.17em}\hspace{0.17em}}cm/se{c}^{2}$

4. $6\text{\hspace{0.17em}\hspace{0.17em}}cm/se{c}^{2}$

Concept Questions :-

Graphs
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The displacement versus time graph for a body moving in a straight line is shown in figure. Which of the following regions represents the motion when no force is acting on the body

(1) ab

(2) bc

(3) cd

(4) de

Concept Questions :-

Graphs
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The $x-t$ graph shown in figure represents

(1) Constant velocity

(2) Velocity of the body is continuously changing

(3) Instantaneous velocity

(4) The body travels with constant speed upto time t1 and then stops

Concept Questions :-

Graphs