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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When a man walks on a horizontal road with velocity 1 km/h, the rain appears to him coming vertically at a speed of 2 km/h. The actual speed of the rain with respect to ground is:

1. 3 km/h

2. 5 km/h

3. 1 km/h

4. 3 km/h

Subtopic:  Relative Motion |
 72%
From NCERT
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A body started moving with an initial velocity of \(4\) m/s along the east and an acceleration \(1\) m/s2 along the north. The velocity of the body just after \(4\) s will be?

1. \(8\) m/s along East
2. \(4 \sqrt{2} \) m/s along North-East
3. \(8\) m/s along North
4. \(4 \sqrt{2} \) m/s along South-East

Subtopic:  Uniformly Accelerated Motion |
 78%
From NCERT
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A particle is thrown obliquely at \(t=0\). The particle has the same K.E. at \(t=5\) seconds and at \(t=9\) seconds. The particle attains maximum altitude at:
1. \(t=6\) s
2. \(t=7\) s
3. \(t=8\) s
4. \(t=14\) s

Subtopic:  Projectile Motion |
 75%
From NCERT
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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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