A body starts moving from rest on a horizontal ground such that the position vector of the body with respect to its starting point is given by r = 2ti^ + 3t2j^. The equation of the trajectory of the body is:

1. y = 1.5 x

2. y = 0.75 x2

3. y = 1.5 x2

4. y = 0.45 x2

Subtopic:  Position & Displacement |
 66%
From NCERT
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A particle starts moving with constant acceleration with initial velocity (\(\hat{\mathrm{i}}+5\hat{\mathrm{j}}\)) m/s. After \(4\) seconds, its velocity becomes (\(3\hat{\mathrm{i}}-2\hat{\mathrm{j}}\)) m/s. The magnitude of its displacement in 4 seconds is:
1. \(5\) m
2. \(10\) m
3. \(15\) m
4. \(20\) m

Subtopic:  Uniformly Accelerated Motion |
 65%
From NCERT
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If a particle is moving in a circular orbit with constant speed, then:

1. its velocity is variable.
2. its acceleration is variable.
3. its angular momentum is constant.
4. All of the above

Subtopic:  Circular Motion |
 77%
From NCERT
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A projectile is projected with initial kinetic energy K. If it has kinetic energy 0.25K at its highest point, then the angle of projection is:

1. 30°

2. 45°

3. 60°

4. 75°

Subtopic:  Projectile Motion |
 67%
From NCERT
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If position of a particle varies according to the equations x = 3t2, y = 2t, and z = 4t + 4, then which of the following is incorrect?

1. Velocities in y and z directions are constant
2. Acceleration in the x-direction is non-uniform
3. Acceleration in the x-direction is uniform
4. Motion is not in a straight line

Subtopic:  Acceleration |
 74%
From NCERT
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If three coordinates of a particle change according to the equations x=3t2, y=2t, z=4, then the magnitude of the velocity of the particle at time \(t=1\) second will be:
1. 211 unit 

2. 34 unit

3. \(40\) unit

4. 210 unit

Subtopic:  Speed & Velocity |
 80%
From NCERT
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In a uniform circular motion, if the speed of the particle is 2 m/s and radius of the circle is 2 m, then the values of centripetal and tangential acceleration are, respectively:

1. 2 m/s2, 2 m/s2

2. 2 m/s2, 1 m/s2

3. 0, 2 m/s2

4. 2 m/s2, 0

Subtopic:  Circular Motion |
 75%
From NCERT
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A person, who can swim with speed u relative to water, wants to cross a river (of width d and water is flowing with speed v). The minimum time in which the person can do so is:

1.  dv

2.  du

3.  dv2 + u2

4.  dv2 - u2

Subtopic:  Relative Motion |
From NCERT
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The position vector of a particle r as a function of time t (in seconds) is r = 3ti^ + 2t2j^ m. The initial acceleration of the particle is:

1. 2 m/s2

2. 3 m/s2

3. 4 m/s2

4. Zero

Subtopic:  Acceleration |
 87%
From NCERT
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Coordinates of a particle as a function of time t are x = 2t, y = 4t. It can be inferred that the path of the particle will be:

1. Straight line

2. Ellipse

3. Parabola

4. Hyperbola

Subtopic:  Position & Displacement |
 74%
From NCERT
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