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 . The equation of the trajectory of the body is:
1. y = 1.5 x
2. y = 0.75
3. y = 1.5
4. y = 0.45
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
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 |
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°
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