A particle is moving with veocity ; where k is constant. The general equation for the path is:
1.
2.
3.
4. xy=constant
In \(1.0\) s, a particle goes from point A to point B, moving in a semicircle of radius \(1.0\) m (see figure). The magnitude of the average velocity is:
1. \(3.14\) m/s
2. \(2.0\) m/s
3. \(1.0\) m/s
4. zero
The coordinates of a moving particle at any time ‘t’ are given by x = αt3 and y = βt3. The speed of the particle at time ‘t’ is given by:
1.
2.
3.
4.
A particle is moving such that its position coordinates (x, y) are (2m, 3m) at time t = 0, (6m, 7m) at time t = 2s and (13m, 14m) at time t = 5s. Average velocity vector (vav) from t = 0 to t = 5s is
1. (13+14)
2. (+)
3. 2(+)
4. (+)
The coordinates of a moving particle at a time t, are given by, x = 5sin10t, y = 5cos10t. The speed of the particle is:
(1) 25
(2) 50
(3) 10
(4)
A car turns at a constant speed on a circular track of radius \(100\) m, taking \(62.8\) s for every circular lap. The average velocity and average speed for each circular lap, respectively, is:
1. | \(0,~0\) | 2. | \(0,~10\) m/s |
3. | \(10\) m/s, \(10\) m/s | 4. | \(10\) m/s, \(0\) |
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
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.
3.
4.
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. | \(75^\circ\) |
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. |