A body thrown vertically so as to reach its maximum height in t second. The total time from the time of projection to reach a point at half of its maximum height while returning (in second) is:

1. $\sqrt{2}t$

2. $\left(1+\frac{1}{\sqrt{2}}\right)t$

3. $\frac{3t}{2}$

4. $\frac{t}{\sqrt{2}}$

Subtopic:  Uniformly Accelerated Motion |
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A stone falls freely from rest from a height h and it travels a distance $\frac{9h}{25}$ in the last second. The value of h is:

1. 145 m

2. 100 m

3. 122.5 m

4. 200 ms

Subtopic:  Uniformly Accelerated Motion |
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A point moves in a straight line under the retardation a${\mathrm{v}}^{2}$. If the initial velocity is u, the distance covered in 't' seconds is-

1.  $\mathrm{aut}$

2.

3.

4.

Subtopic:  Non Uniform Acceleration |
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A particle is thrown upwards from ground. It experiences a constant resistance force which can produce retardation of 2 $m/{s}^{2}$. The ratio of time of ascent to the time of descent is:

(1) 1:1

(2) $\sqrt{\frac{2}{3}}$

(3) $\frac{2}{3}$

(4) $\sqrt{\frac{3}{2}}$

Subtopic:  Uniformly Accelerated Motion |
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Two men P & Q are standing at corners A & B of square ABCD of side 8 m. They start moving along the track with constant speed 2 m/s and 10 m/s respectively. The time when they will meet for the first time, is equal to:

(1) 2 sec

(2) 3 sec

(3) 1 sec

(4) 6 sec

Subtopic:  Relative Motion in One Dimension |
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A bullet loses $\frac{1}{20}$ of its velocity passing through a plank. The least number of planks required to stop the bullet is (All planks offers same retardation)

(1) 10

(2) 11

(3) 12

(4) 23

Subtopic:  Uniformly Accelerated Motion |
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A body starts from the origin and moves along the X-axis such that the velocity at any instant is given by $\left(4{t}^{3}-2t\right)$, where t is in sec and velocity in m/s. What is the acceleration of the particle, when it is 2 m from the origin ?

1. 28 m/s2

2. 22 m/s2

3. 12 m/s2

4. 10 m/s2

Subtopic:  Non Uniform Acceleration |
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The relation between time and distance is $t=\alpha {x}^{2}+\beta x$, where α and β are constants. The retardation is

1. $2\alpha {v}^{3}$

2. $2\beta {v}^{3}$

3. $2\alpha \beta {v}^{3}$

4. $2{\beta }^{2}{v}^{3}$

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
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A point moves with uniform acceleration and v1, v2 and v3 denote the average velocities in the three successive intervals of time t1, t2 and t3. Which of the following relations is correct ?

(1) $\left({v}_{1}-{v}_{2}\right):\left({v}_{2}-{v}_{3}\right)=\left({t}_{1}-{t}_{2}\right):\left({t}_{2}+{t}_{3}\right)$

(2) $\left({v}_{1}-{v}_{2}\right):\left({v}_{2}-{v}_{3}\right)=\left({t}_{1}+{t}_{2}\right):\left({t}_{2}+{t}_{3}\right)$

(3) $\left({v}_{1}-{v}_{2}\right):\left({v}_{2}-{v}_{3}\right)=\left({t}_{1}-{t}_{2}\right):\left({t}_{1}-{t}_{3}\right)$

(4) $\left({v}_{1}-{v}_{2}\right):\left({v}_{2}-{v}_{3}\right)=\left({t}_{1}-{t}_{2}\right):\left({t}_{2}-{t}_{3}\right)$

Subtopic:  Uniformly Accelerated Motion |
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The acceleration of a moving body can be found from

(1) Area under velocity-time graph

(2) Area under distance-time graph

(3) Slope of the velocity-time graph

(4) Slope of distance-time graph

Subtopic:  Graphs |
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