# 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 particle is moving such that its position coordinates (x, y) are ($$2$$ m, $$3$$ m) at time $$t=0,$$ ($$6$$ m,$$7$$ m) at time $$t=2$$ s, and ($$13$$ m, $$14$$ m) at time $$t=$$ $$5$$ s. The average velocity vector $$\vec{v}_{avg}$$ from $$t=$$ 0 to $$t=$$ $$5$$ s is:
1. $${1 \over 5} (13 \hat{i} + 14 \hat{j})$$
2. $${7 \over 3} (\hat{i} + \hat{j})$$
3. $$2 (\hat{i} + \hat{j})$$
4. $${11 \over 5} (\hat{i} + \hat{j})$$

Subtopic:  Average Speed & Average Velocity |
76%
From NCERT
AIPMT - 2014
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A stone falls freely under gravity. It covers distances $$h_1,~h_2$$ and $$h_3$$ in the first $$5$$ seconds, the next $$5$$ seconds and the next $$5$$ seconds respectively. The relation between $$h_1,~h_2$$ and $$h_3$$ is:

 1 $$h_1=\frac{h_2}{3}=\frac{h_3}{5}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$$ 2 $$h_2=3h_1$$ and $$h_3=3h_2$$ 3 $$h_1=h_2=h_3$$ 4 $$h_1=2h_2=3h_3$$
Subtopic:  Uniformly Accelerated Motion |
82%
From NCERT
AIPMT - 2013
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A particle has initial velocity $$\left(2 \hat{i} + 3 \hat{j}\right)$$ and acceleration $$\left(0 . 3 \hat{i} + 0 . 2 \hat{j}\right)$$. The magnitude of velocity after $$10$$ s will be:

1. $$9 \sqrt{2}~ \text{units}$$
2. $$5 \sqrt{2} ~\text{ units}$$
3. $$5~\text{units}$$
4. $$9~\text{units}$$

Subtopic:  Uniformly Accelerated Motion |
87%
From NCERT
AIPMT - 2012
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The motion of a particle along a straight line is described by the equation $$x = 8+12t-t^3$$ where $$x$$ is in meter and $$t$$ in seconds. The retardation of the particle, when its velocity becomes zero, is:
1. $$24$$ ms-2
2. zero
3. $$6$$ ms-2
4. $$12$$ ms-2

Subtopic:  Acceleration |
75%
From NCERT
AIPMT - 2012
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A boy standing at the top of a tower of 20 m height drops a stone. Assuming $$g=$$ 10 ms-2, the velocity with which it hits the ground is:
 1 20 m/s 2 40 m/s 3 5 m/s 4 10 m/s
Subtopic:  Uniformly Accelerated Motion |
91%
From NCERT
AIPMT - 2011
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A ball is dropped from a high-rise platform at $$t=0$$ starting from rest. After $$6$$ seconds, another ball is thrown downwards from the same platform with speed $$v$$. The two balls meet after $$18$$ seconds. What is the value of $$v$$?

 1 $$75$$ ms-1 2 $$55$$ ms-1 3 $$40$$ ms-1 4 $$60$$ ms-1
Subtopic:  Uniformly Accelerated Motion |
58%
From NCERT
AIPMT - 2010
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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. (velocity)$$3/2$$
2. (distance)$$2$$
3. (distance)$$-2$$
4. (velocity)$$2/3$$

Subtopic:  Acceleration |
70%
From NCERT
AIPMT - 2010
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A bus is moving at a speed of $$10$$ ms-1 on a straight road. A scooterist wishes to overtake the bus in $$100$$ s. If the bus is at a distance of $$1$$ km from the scooterist, with what speed should the scooterist chase the bus?
1. $$20$$ ms-1
2. $$40$$ ms-1
3. $$25$$ ms-1
4. $$10$$ ms-1
Subtopic:  Relative Motion in One Dimension |
77%
From NCERT
AIPMT - 2009
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