# A particle moves along a straight line and its position as a function of time is given by$\mathrm{}$ $$x= t^3-3t^2+3t+3$$ then particle: 1.  stops at $$t=1~\text{s}$$ and reverses its direction of motion. 2.  stops at $$t= 1~\text{s}$$ and continues further without a change of direction. 3.  stops at $$t=2~\text{s}$$ and reverses its direction of motion. 4.  stops at $$t=2~\text{s}$$ and continues further without a change of direction.

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
51%
From NCERT
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If the velocity of a particle is $$v=At+Bt^{2},$$ where $$A$$ and $$B$$ are constants, then the distance travelled by it between $$1~\text{s}$$ and $$2~\text{s}$$ is:

 1 $$3A+7B$$ 2 $$\frac{3}{2}A+\frac{7}{3}B$$ 3 $$\frac{A}{2}+\frac{B}{3}$$ 4 $$\frac{3A}{2}+4B$$
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
88%
From NCERT
NEET - 2016
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A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to $$v(x)= βx^{- 2 n}$$ where $$\beta$$ and $$n$$ are constants and $$x$$ is the position of the particle. The acceleration of the particle as a function of $$x$$ is given by:
1. $$- 2 nβ^{2} x^{- 2 n - 1}$$
2. $$- 2 nβ^{2} x^{- 4 n - 1}$$
3. $$- 2 \beta^{2} x^{- 2 n + 1}$$
4. $$- 2 nβ^{2} x^{- 4 n + 1}$$
${}^{}$

Subtopic:  Non Uniform Acceleration |
68%
From NCERT
NEET - 2015
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A car moves from $$X$$ to $$Y$$ with a uniform speed $$v_u$$ and returns to $$X$$ with a uniform speed $$v_d.$$ The average speed for this round trip is:

 1 $$\frac{2 v_{d} v_{u}}{v_{d} + v_{u}}$$ 2 $$\sqrt{v_{u} v_{d}}$$ 3 $$\frac{v_{d} v_{u}}{v_{d} + v_{u}}$$ 4 $$\frac{v_{u} + v_{d}}{2}$$
Subtopic:  Average Speed & Average Velocity |
82%
From NCERT
AIPMT - 2007
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The coordinate of an object is given as a function of time by $$x = 7 t - 3 t^{2}$$, where $$x$$ is in metres and $$t$$ is in seconds. Its average velocity over the interval $$t=0$$ to $$t=4$$ is will be:
1. $$5$$ m/s
2. $$-5$$ m/s
3. $$11$$ m/s
​​​​​​​4. $$-11$$ m/s

Subtopic:  Average Speed & Average Velocity |
72%
From NCERT
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The displacement time graph of a moving particle is shown in the figure below. The instantaneous velocity of the particle is negative at the point:

 1 D 2 F 3 C 4 E
Subtopic:  Graphs |
86%
From NCERT
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A boy standing at the top of a tower of $$20$$ m height drops a stone. Assuming $$g=10$$ m/s2, the velocity with which it hits the ground will be:
1. $$20$$ m/s
2. $$40$$ m/s
3. $$5$$ m/s
4. $$10$$ m/s

Subtopic:  Uniformly Accelerated Motion |
90%
From NCERT
NEET - 2011
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A particle moves along a path $$ABCD$$ as shown in the figure. The magnitude of the displacement of the particle from $$A$$ to $$D$$ is:

1. $\left(5+10\sqrt{2}\right)$m
2. $$10$$ m
3. $15\sqrt{2}$ m
4. $$15$$ m

Subtopic:  Distance & Displacement |
70%
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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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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