Two particles having position vectors \(\overrightarrow{r_{1}} = \left( 3 \hat{i} + 5 \hat{j}\right)\) metres and \(\overrightarrow{r_{2}} = \left(- 5 \hat{i} - 3 \hat{j} \right)\) metres are moving with velocities \(\overrightarrow{v}_{1} = \left( 4 \hat{i} + 3 \hat{j}\right)\)\(\text{m/s}\) and \(\overrightarrow{v}_{2} = \left(\alpha\hat{i} + 7 \hat{j} \right)\)\(\text{m/s}\). If they collide after \(2\) seconds, the value of \(\alpha\) is:

1. \(2\) 2. \(4\)
3. \(6\) 4. \(8\)

Subtopic:  Relative Motion |
 51%
From NCERT
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A batsman hits a sixer and the ball touches the ground outside the cricket field. Which of the following graph describes the variation of the cricket ball's vertical velocity \(v\) with time between the time \(t_1\) as it hits the bat and time \(t_2\) when it touches the ground:

1. 2.
3. 4.

Subtopic:  Projectile Motion |
 59%
From NCERT
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The \(x\) and \(y\) coordinates of the particle at any time are \(x = 5t-2t^2\) and \(y=10t\) respectively, where \(x\) and \(y\) are in metres and \(t\) is in seconds. The acceleration of the particle at \(t=2\) s is:
1. \(0\) m/s2
2. \(5\) m/s2
3. \(-4\) m/s2
4. \(-8\) m/s2

Subtopic:  Acceleration |
 84%
From NCERT
NEET - 2017
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Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t1. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t2. The time taken by her to walk up on the moving escalator will be 

1. t1-t22

2. t1t2t2-t1

3. t1t2t2+t1

4. t1-t2

Subtopic:  Relative Motion |
 76%
From NCERT
NEET - 2017
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A particle moves so that its position vector is given by \(r=\cos \omega t \hat{x}+\sin \omega t \hat{y}\) where \(\omega\) is a constant. Based on the information given, which of the following is true?

1. The velocity and acceleration, both are parallel to \(r.\)
2. The velocity is perpendicular to \(r\) and acceleration is directed towards the origin.
3. The velocity is not perpendicular to \(r\) and acceleration is directed away from the origin.
4. The velocity and acceleration, both are perpendicular to \(r.\)
Subtopic:  Acceleration |
 70%
From NCERT
NEET - 2016
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A particle of mass 10g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration, if the kinetic energy of the particle becomes equal to 8x10-4 J by the end of the second revolution after the beginning of the motion?

(1) 0.15 m/s2

(2) 0.18 m/s2

(3) 0.2 m/s2

(4) 0.1 m/s2

Subtopic:  Circular Motion |
From NCERT
NEET - 2016
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A projectile is fired from the surface of the earth with a velocity of 5 m/s and angle θ with the horizontal. Another projectile fired from another planet with a velocity of 3 m/s at the same angle follows a trajectory, which is identical to the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet (in m/s2) is: [Given, g = 9.8 m/s2]

1. 3.5

2. 5.9

3. 16.3

4. 110.8

 

Subtopic:  Projectile Motion |
 70%
From NCERT
NEET - 2014
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A particle is moving such that its position coordinates (x, y) are (2m, 3m) at time t = 0, (6m, 7m) at time t = 2s and (13m, 14m) at time t = 5s. Average velocity vector (vav) from t = 0 to t = 5s is

1. 15(13i^+14j^)

2. 73(i^+j^)

3. 2(i^+j^)

4. 115(i^+j^)

Subtopic:  Speed & Velocity |
 80%
From NCERT
NEET - 2014
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The velocity of a projectile at the initial point A is (2i + 3j) m/s. Its velocity (in m/s) at point B is:


1.  -2i+3j

2.  -2i-3j

3.   2i-3j

4.  2i+3j

Subtopic:  Projectile Motion |
 79%
From NCERT
NEET - 2013
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The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is:

1. θ=tan-114                                       

2. θ=tan-14

3. θ=tan-12                                         

4. θ=45°

Subtopic:  Projectile Motion |
 74%
From NCERT
NEET - 2012
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