# A point moves in a straight line so that its displacement is $$x$$ m at time $$t$$ sec, given by ${\mathrm{}}^{}$$$x^2= t^2+1$$. Its acceleration in $$\text{m/s}^2$$ at time $$1$$ sec is: 1. $$\frac{1}{x}$$ 2. $$\frac{1}{x} - \frac{1}{x^{3}}$$ 3. $$\frac{2}{x}$$ 4. $$-\frac{t^2}{x^3}$$

Subtopic:  Acceleration |
50%
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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 in a straight line, according to the law $$x=4a[t+a\sin(t/a)],$$ where $$x$$ is its position in metres, $$t$$ is in seconds & $$a$$ is some constant, then the velocity is zero at:

 1 $$x = 4 a^2\pi$$ metres 2 $$t = \pi$$ sec 3 $$t =0$$ sec 4 none of the above
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
From NCERT
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A particle shows distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point:

1. B

2. C

3. D

4. A

Subtopic:  Graphs |
73%
From NCERT
NEET - 2008
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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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 Assertion (A): Displacement of a body may be zero when distance travelled by it is not zero. Reason (R): The displacement is the longest distance between initial and final position.

 1 Both (A) and (R) are True and (R) is the correct explanation of (A). 2 Both (A) and (R) are True but (R) is not the correct explanation of (A). 3 (A) is True but (R) is False. 4 Both (A) and (R) are False.
Subtopic:  Distance & Displacement |
85%
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Two cars $$A$$ and $$B$$ are travelling in the same direction with velocities $$v_1$$ and $$v_2$$ $$(v_1>v_2).$$ When the car $$A$$ is at a distance $$d$$ behind car $$B$$, the driver of the car $$A$$ applied the brake producing uniform retardation $$a$$. There will be no collision when:
1. $$d < \frac{\left( v_{1} - v_{2} \right)^{2}}{2 a}$$
2. $$d < \frac{v_{1}^{2} - v_{2}^{2}}{2 a}$$
3. $$d > \frac{\left(v_{1} - v_{2}\right)^{2}}{2 a}$$
4. $$d > \frac{v_{1}^{2} - v_{2}^{2}}{2 a}$$

Subtopic:  Relative Motion in One Dimension |
59%
From NCERT
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Which of the following four statements is false?

 1 A body can have zero velocity and still be accelerated. 2 A body can have a constant velocity and still have a varying speed. 3 A body can have a constant speed and still have a varying velocity. 4 The direction of the velocity of a body can change when its acceleration is constant.

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
66%
From NCERT
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The initial velocity of a particle is $$u$$ (at $$t=0$$) and the acceleration $$f$$ is given by $$at$$. Which of the following relation is valid?
1. $$v = u + a t^{2}$$
2. $$v = u + a \frac{t^{2}}{2}$$
3. $$v = u + a t$$
4. $$v= u$$

Subtopic:  Non Uniform Acceleration |
From NCERT
PMT - 1981
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A stone falls freely from rest from a height $$h$$ and it travels a distance of $$\frac{9 h}{25}$$ 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 |
71%
From NCERT
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