If position of a particle varies according to the equations x = 3, 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 |
If three coordinates of a particle change according to the equations , then the magnitude of the velocity of the particle at time \(t=1\) second will be:
1. unit
2. unit
3. \(40\) unit
4. unit
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 , 2
2. 2 , 1
3. 0, 2
4. 2 , 0
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.
2.
3.
4.
The position vector of a particle as a function of time t (in seconds) is . The initial acceleration of the particle is:
1. 2
2. 3
3. 4
4. Zero
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
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. km/h
2. km/h
3. 1 km/h
4. 3 km/h
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 |
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
The position vector of a particle is . 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. |