A vehicle travels half the distance with speed $$v$$ and the remaining distance with speed $$2v$$. Its average speed is:
1. $$\frac{3v}{4}$$
2. $$\frac{v}{3}$$
3. $$\frac{2v}{3}$$
4. $$\frac{4v}{3}$$
Subtopic:  Average Speed & Average Velocity |
65%
From NCERT
NEET - 2023
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A person travelling in a straight line moves with a constant velocity $$v_1$$ for a certain distance $$x$$ and with a constant velocity $$v_2$$ ${}_{}$for the next equal distance. The average velocity $$v$$ is given by the relation:

 1 $$\frac{1}{v} = \frac{1}{v_1}+\frac{1}{v_2}$$ 2 $$\frac{2}{v} = \frac{1}{v_1}+\frac{1}{v_2}$$ 3 $$\frac{v}{2} = \frac{v_1+v_2}{2}$$ 4 $$v = \sqrt{v_1v_2}$$

Subtopic:  Average Speed & Average Velocity |
77%
From NCERT
NEET - 2019
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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. The average velocity vector $$\vec{v}_{avg}$$ from $$t=$$ 0 to $$t=$$ $$5$$ s is:
1. $${1 \over 5} (13 \hat{i} + 14 \hat{j})$$
2. $${7 \over 3} (\hat{i} + \hat{j})$$
3. $$2 (\hat{i} + \hat{j})$$
4. $${11 \over 5} (\hat{i} + \hat{j})$$

Subtopic:  Average Speed & Average Velocity |
76%
From NCERT
AIPMT - 2014
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A particle covers half of its total distance with speed ν1 and the rest half distance with speed ν2.
Its average speed during the complete journey is:

1. $\frac{{v}_{1}+{v}_{2}}{2}$

2. $\frac{{v}_{1}{v}_{2}}{{v}_{1}+{v}_{2}}$

3. $\frac{2{v}_{1}{v}_{2}}{{v}_{1}+{v}_{2}}$

4. $\frac{{v}_{1}^{2}{v}_{2}^{2}}{{v}_{1}^{2}+{v}_{2}^{2}}$

Subtopic:  Average Speed & Average Velocity |
89%
From NCERT
AIPMT - 2011
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A car moves from $$\mathrm{X}$$ to $$\mathrm{Y}$$ with a uniform speed $$\mathrm{v_u}$$ and returns to $$\mathrm{X}$$ with a uniform speed $$\mathrm{v_d}.$$ The average speed for this round trip is:

1. $\frac{2{\mathrm{v}}_{\mathrm{d}}{\mathrm{v}}_{\mathrm{u}}}{{\mathrm{v}}_{\mathrm{d}}+{\mathrm{v}}_{\mathrm{u}}}$

2. $\sqrt{{\mathrm{v}}_{\mathrm{u}}{\mathrm{v}}_{\mathrm{d}}}$

3. $\frac{{\mathrm{v}}_{\mathrm{d}}{\mathrm{v}}_{\mathrm{u}}}{{\mathrm{v}}_{\mathrm{d}}+{\mathrm{v}}_{\mathrm{u}}}$

4. $\frac{{\mathrm{v}}_{\mathrm{u}}+{\mathrm{v}}_{\mathrm{d}}}{2}$

Subtopic:  Average Speed & Average Velocity |
82%
From NCERT
AIPMT - 2007
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A particle starts from rest with constant acceleration. The ratio of space-average velocity to the time-average velocity is:

where time-average velocity and space-average velocity, respectively, are defined as follows:

$}_{time}$ $=$ $\frac{\int vdt}{\int dt}$
$}_{space}$ $=$ $\frac{\int vds}{\int ds}$

 1 1/2 2 3/4 3 4/3 4 3/2
Subtopic:  Average Speed & Average Velocity |
From NCERT
AIPMT - 1999
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