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. | \(\frac{11}{5}\left ( \hat{i}+\hat{j} \right )\) |
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:
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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:
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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:
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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 |
A bus is going to the North at a speed of 30 kmph. It makes a 90° left turn without changing the speed. The change in the velocity of the bus is:
1. | 30 kmph towards W |
2. | 30 kmph towards S-W |
3. | 42.4 kmph towards S-W |
4. | 42.4 kmph towards N-W |
Three particles are moving with constant velocities and v respectively as given in the figure. After some time, if all the three particles are in the same line, then the relation among and v is:
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