# 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 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 |
56%
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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The displacement of a particle is given by $\mathrm{y}=\mathrm{a}+\mathrm{bt}+{\mathrm{ct}}^{2}-{\mathrm{dt}}^{4}$. The initial velocity and acceleration are, respectively:

 1 $$\mathrm{b}, ~\mathrm{-4d}$$ 2 $$\mathrm{-b},~ \mathrm{2c}$$ 3 $$\mathrm{b}, ~\mathrm{2c}$$ 4 $$\mathrm{2c}, ~\mathrm{-2d}$$
Subtopic:  Non Uniform Acceleration |
81%
From NCERT
PMT - 1999
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An elevator car, whose floor to ceiling distance is equal to 2.7 m, starts ascending with constant acceleration of 1.2 ms–2. 2 sec after the start, a bolt begins falling from the ceiling of the car. The free fall time of the bolt is

1. $\sqrt{0.54}$ $s$

2. $\sqrt{6}$ $s$

3. 0.7 s

4. 1 s

Subtopic:  Relative Motion in One Dimension |
From NCERT
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The acceleration ‘a’ in m/s2 of a particle is given by $a=3{t}^{2}+2t+2$ where t is the time. If the particle starts out with a velocity, u = 2 m/s at t = 0, then the velocity at the end of 2 seconds will be:

1. 12 m/s

2. 18 m/s

3. 27 m/s

4. 36 m/s

Subtopic:  Acceleration |
72%
From NCERT
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A particle moves along a straight line such that its displacement at any time t is given by $\mathrm{S}={\mathrm{t}}^{3}-6{\mathrm{t}}^{2}+3\mathrm{t}+4$ metres. The velocity when the acceleration is zero is:

 1 4 ms-1 2 −12 ms−1 3 42 ms−1 4 −9 ms−1
Subtopic:  Acceleration |
81%
From NCERT
PMT - 1994
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The position $$x$$ of a particle varies with time $$t$$ as $$x=at^2-bt^3$$. The acceleration of the particle will be zero at time $$t$$ equal to:

 1 $$\dfrac{a}{b}$$ 2 $$\dfrac{2a}{3b}$$ 3 $$\dfrac{a}{3b}$$ 4 zero

Subtopic:  Acceleration |
84%
From NCERT
PMT - 1997
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The relation $$3t = \sqrt{3x} + 6$$ describes the displacement of a particle in one direction where $$x$$ is in metres and $$t$$ in seconds. The displacement, when velocity is zero, is:

 1 $$24$$ metres 2 $$12$$ metres 3 $$5$$ metres 4 zero
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
76%
From NCERT
PMT - 2000
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