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. $\frac{1}{5}$(13$\stackrel{^}{i}$+14$\stackrel{^}{j}$)

2. $\frac{7}{3}$($\stackrel{^}{i}$+$\stackrel{^}{j}$)

3. 2($\stackrel{^}{i}$+$\stackrel{^}{j}$)

4. $\frac{11}{5}$($\stackrel{^}{i}$+$\stackrel{^}{j}$

Subtopic:  Speed & Velocity |
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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. $2\sqrt{11}$ unit

2. $\sqrt{34}$ unit

3. 40 unit

4. $2\sqrt{10}$ unit

Subtopic:  Speed & Velocity |
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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

Subtopic:  Speed & Velocity |
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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. $\sqrt{{\alpha }^{2}+{\beta }^{2}}$

2. $3\text{\hspace{0.17em}}t\sqrt{{\alpha }^{2}+{\beta }^{2}}$

3. $3\text{\hspace{0.17em}}{t}^{2}\sqrt{{\alpha }^{2}+{\beta }^{2}}$

4. ${t}^{2}\sqrt{{\alpha }^{2}+{\beta }^{2}}$

Subtopic:  Speed & Velocity |
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A particle moves along the positive branch of the curve y = $\frac{{\mathrm{x}}^{2}}{2}$ where x = $\frac{{\mathrm{t}}^{2}}{2}$, & x and y are measured in metres and in seconds respectively. At = 2s, the velocity of the particle will be

1.

2.

3.

4.

Subtopic:  Speed & Velocity |
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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

Subtopic:  Speed & Velocity |
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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

1.

2.

3.

4.

Subtopic:  Speed & Velocity |
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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:

1. 2

2.  $2\sqrt{3}$

3.  $\sqrt{3}$

4.  $\frac{\sqrt{3}}{2}$

Subtopic:  Speed & Velocity |
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A particle moves on the curve . The angle of its velocity vector with the x-axis at the point  will be:

1. 30$°$

2. 60$°$

3. 45$°$

4. 75$°$

Subtopic:  Speed & Velocity |
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The position of a particle is given by  where t is in seconds and the coefficients have the proper units for r to be in meters. The magnitude and direction of $\stackrel{\to }{\mathrm{v}\left(\mathrm{t}\right)}$ at t = 1.0 s are:

1.  4 m/s at ${53}^{ο}$ with x-axis

2.  4 m/s at ${37}^{ο}$ with x-axis

3.  5 m/s at ${53}^{ο}$ with y-axis

4.  5 m/s at ${53}^{ο}$ with x-axis

Subtopic:  Speed & Velocity |
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