The position vector of a particle is r = a sin ωti^ + a cos ωtj^. The velocity of the particle is:

1.  parallel to the position vector.
2.  at 60° with position vector.
3.  parallel to the acceleration vector.
4.  perpendicular to the position vector.

Subtopic:  Circular Motion |
 79%
From NCERT
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A projectile is projected from the ground with the velocity v0 at an angle θ with the horizontal. What is the vertical component of the velocity of the projectile when its vertical displacement is equal to half of the maximum height attained?

1.  3v0 cosθ

2.  v02sin θ

3.  v02cosθ

4.  5v0

Subtopic:  Projectile Motion |
 70%
From NCERT
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A particle starts moving on a circular path from rest, such that its tangential acceleration varies with time as \(a_t=kt\). Distance traveled by particle on the circular path in time \(t\) is:
1. \( \frac{kt^3}{3} \)
2. \(\frac{kt^2}{6} \)
3. \(\frac{kt^3}{6} \)
4. \(\frac{k t^2}{2}\)

Subtopic:  Circular Motion |
 71%
From NCERT
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The speed of water in a river is 4 km/h and a man can swim at 5 km/h. The minimum time taken by the man to cross the river of width 200 m is:

1.  15 h

2.  125 h

3.  115 h

4.  120 h

Subtopic:  Relative Motion |
 57%
From NCERT
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A particle is moving on a circular path of radius \(R.\) When the particle moves from point \(A\) to \(B\) (angle \( \theta\)), the ratio of the distance to that of the magnitude of the displacement will be:

         

1. θsinθ2

2. θ2sinθ2

3. θ2cosθ2

4. θcosθ2

Subtopic:  Position & Displacement |
 74%
From NCERT
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Two particles move from A to C and A to D on a circle of radius R and diameter AB. If the time taken by both particles are the same, then the ratio of magnitudes of their average velocities is:
                                
1. 2

2.  23

3.  3

4.  32

Subtopic:  Speed & Velocity |
 62%
From NCERT
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A particle moves on the curve \(x^2 = 2y\). The angle of its velocity vector with the x-axis at the point \(\left(1, \frac{1}{2}\right )\) will be:

1. \(30^\circ\) 2. \(60^\circ\)
3. \(45^\circ\) 4. \(75^\circ\)
Subtopic:  Speed & Velocity |
 61%
From NCERT
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A particle is moving along a curve. Select the correct statement.

1. If its speed is constant, then it has no acceleration.
2. If its speed is increasing, then the acceleration of the particle is along its direction of motion.
3. If its speed is decreasing, then the acceleration of the particle is opposite to its direction of motion.
4. If its speed is constant, its acceleration is perpendicular to its velocity.
Subtopic:  Acceleration |
 68%
From NCERT
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A car is moving along east at 10 m/s and a bus is moving along north at 10 m/s. The velocity of the car with respect to the bus is along:

1. North-East 2. South-East
3. North-West 4. South-West
Subtopic:  Relative Motion |
 59%
From NCERT
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A particle starts moving from the origin in the XY plane and its velocity after time \(t\) is given by \(\overrightarrow{\mathrm{v}}=4 \hat{\mathrm{i}}+2 \mathrm{t} \hat{\mathrm{j}}\). The trajectory of the particle is correctly shown in the figure:

1. 2.
3. 4.


 

Subtopic:  Speed & Velocity |
 60%
From NCERT
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