# For the following acceleration versus time graph the corresponding velocity versus displacement graph is  1.  2.  3.  4.

Subtopic:  Uniformly Accelerated Motion |
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The displacement x of a particle moving in one dimension under the action of a constant force is related to time t by the equation $t$ $=$ $\sqrt{x}$ $+$ $3$, where x is in metres and t is in seconds. What is the displacement of the particle from t = 0 s to t = 6 s?

1.  0

2.  12 m

3.  6 m

4.  18 m

Subtopic:  Distance & Displacement |
58%
From NCERT
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The acceleration $$a$$ (in ${\mathrm{ms}}^{-2}$) of a body, starting from rest varies with time $$t$$ (in $$\mathrm{s}$$) as per the equation $$a=3t+4.$$ The velocity of the body at time $$t=2$$ $$\mathrm{s}$$ will be:
1. $$10$$ ${\mathrm{ms}}^{-1}$
2. $$18$$ ${\mathrm{ms}}^{-1}$
3. $$14$$ ${\mathrm{ms}}^{-1}$
4. $$26$$ ${\mathrm{ms}}^{-1}$

Subtopic:  Non Uniform Acceleration |
71%
From NCERT
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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 |
57%
From NCERT
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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. 125 m

4. 200 ms

Subtopic:  Uniformly Accelerated Motion |
69%
From NCERT
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A point moves in a straight line under the retardation a${\mathrm{v}}^{2}$. If the initial velocity is $$\mathrm{u},$$ the distance covered in $$\mathrm{t}$$ seconds is:
1. $\mathrm{aut}$
2. $\frac{1}{\mathrm{a}}\mathrm{ln}$ $\left(\mathrm{aut}\right)$
3. $\frac{1}{\mathrm{a}}\mathrm{ln}$ $\left(1+\mathrm{aut}\right)$
4. $\mathrm{a}$ $\mathrm{ln}$ $\left(\mathrm{aut}\right)$

Subtopic:  Non Uniform Acceleration |
57%
From NCERT
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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 |
From NCERT
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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 |
60%
From NCERT
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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 |
63%
From NCERT
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The relation between time and distance is given by $t=\alpha {x}^{2}+\beta x$, where α and β are constants. The retardation, as calculated based on this equation, will be (assume v to be velocity) :

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 |
52%
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