A particle is moving such that its position coordinates \((x,y)\) are \((2\) m, \(3\) m) at time \(t=0,\) \((6\) m, \(7\) m) at time \(t=2\) s and \((13\) m, \(14\) m) at time \(t=5\) s. Average velocity vector \((v_{avg})\) from \(t=0\) to \(t=5\) s is:
1. | \(\frac{1}{5}\left ( 13\hat{i}+14\hat{j} \right )\) | 2. | \(\frac{7}{3}\left ( \hat{i}+\hat{j} \right )\) |
3. | \(2\left ( \hat{i}+\hat{j} \right )\) | 4. | \(\frac{11}{5}\left ( \hat{i}+\hat{j} \right )\) |
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
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, \(0\)
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 moves along the positive branch of the curve y = \(\frac{x^{2}}{2}\) where x = \(\frac{t^{2}}{2}\), & x and y are measured in metres and in seconds respectively. At t = 2s, the velocity of the particle will be:
1. \(\left(\right. 2 \hat{i} - 4 \hat{j})\ m / s\)
2. \(\left(\right. 4 \hat{i} + 2 \hat{j}\left.\right) m / s\)
3. \(\left(\right. 2 \hat{i} + 4 \hat{j}\left.\right) m / s\)
4. \(\left(\right. 4 \hat{i} - 2 \hat{j}\left.\right) m / s\)
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 |
Two particles A and B, move with constant velocities \(\vec{v_1}\) and \(\vec{v_2}\) . At the initial moment their position vector are \(\vec{r_1}\) and \(\vec{r_2}\) respectively. The condition for particles A and B for their collision to happen will be:
1.
2.
3.
4.
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. | \(75^\circ\) |
The position of a particle is given by; \(\vec{r}=(3.0t\hat{i}-2.0t^{2}\hat{j}+4.0\hat{k})\) m
where \(t\) is in seconds and the coefficients have the proper units for \(r\) to be in meters. The magnitude and direction of \(\vec{v}(t)\) at \(t=1.0\) s are:
1. | \(4\) m/s \(53^\circ\) with x-axis |
2. | \(4\) m/s \(37^\circ\) with x-axis |
3. | \(5\) m/s \(53^\circ\) with y-axis |
4. | \(5\) m/s \(53^\circ\) with x-axis |