Average velocity

Q.

A man walks $7km$ in $2hours$ and $2km$ in $1hour$ in the same direction. What is mans average velocity for the whole journey?

Q.

The ratio of the numerical values of the average velocity and average speed of a body is always.

1. Unity

2. Unity or less

3. Unity or more

4. Less than unity

Q. Three particles start simultaneously from a point on a horizontal smooth plane. First particle moves with speed $v_1$ towards east, second particle moves towards north with speed $v_2$ and third-one moves towards north east. The velocity of the third particle, so that the three always lie on a line, is

1. $\frac{v_1+v_2}{\sqrt{2}}$
2. $\sqrt{v_1{v}_2}$
3. $\frac{v_1{v}_2}{v_1+v_2}$
4. $\sqrt{2}\frac{v_1{v}_2}{v_1+v_2}$

Q. Consider two stones $\text{A}\&\text{B}$ which are being projected as shown with speeds $20\text{m/s}$ and $40\text{m/s}$ respectively as seen by a stationary observer on ground. Find the time when they meet.

1. $2\text{s}$
2. $1\text{s}$
3. $4\text{s}$
4. $3\text{s}$

Q.

A car travels a distance S on a straight road in two hours and then returns to the starting point in the next three hours. Its average velocity is

1. $\frac{S}{5}$

2. $\frac{2S}{5}$

3. $\frac{S}{2}+\frac{S}{3}$

4. None of the above

Q. Three particles start simultaneously from a point on a horizontal smooth plane. First particle moves with speed $v_1$ towards east, second particle moves towards north with speed $v_2$ and third-one moves towards north east. The velocity of the third particle, so that the three always lie on a line, is

1. $\frac{v_1+v_2}{\sqrt{2}}$
2. $\sqrt{v_1{v}_2}$
3. $\frac{v_1{v}_2}{v_1+v_2}$
4. $\sqrt{2}\frac{v_1{v}_2}{v_1+v_2}$

Q. A person travels along a straight road for the first half time with a velocity $v_1$ and the second half time with a velocity $v_2$. Then, the mean or average velocity $\overline{v}$ is given by

1. $\overline{v}=\frac{v_1+v_2}{2}$
2. $\frac{2}{\overline{v}}=\frac{1}{v_1}+\frac{1}{v_2}$
3. $\overline{v}=\sqrt{v_1{v}_2}$
4. $\overline{v}=\sqrt{\frac{v_2}{v_1}}$

Q. A particle moves from the point $(2.0\hat{i}+4.0\hat{j})\text{m},$ at $t=0$, with an initial velocity $(5.0\hat{i}+4.0\hat{j}){\text{ms}}^{-1}$. It is acted upon by a constant acceleration $(4.0\hat{i}+4.0\hat{j}){\text{ms}}^{-2}$. What is the distance of the particle from the origin at time $2\text{s}$?

1. $20\sqrt{2}\text{m}$
2. $10\sqrt{2}\text{m}$
3. $5\text{m}$
4. $15\text{m}$

Q. Two trains $\text{A}$ and $\text{B}$ moving with speed of $36\text{km/hr}$ and $72\text{km/hr}$ respectively in opposite direction. A man moving in train $\text{A}$ with speed of $1.8\text{km/hr}$ opposite to the direction of train $\text{A}$. Find velocity of man as seen from train $\text{B}$ (in $\text{m/s}$).

1. $32\text{m/s}$
2. $29.5\text{m/s}$
3. $32.5\text{m/s}$
4. $28\text{m/s}$

Q. A body covers the first $1/3$ of the distance with a velocity of $2\text{m/s}$, the next $1/3$ with $3\text{m/s}$ and the rest of the distance with $6\text{m/s}$. The average velocity in $\text{m/s}$ for covering the whole distance is (assume that the body travels with constant velocity in all the parts in a straight line)

1. $3$
2. $\frac{11}{3}$
3. $\frac{8}{3}$
4. $\frac{4}{3}$

Q. Between the two stations, a train uniformly accelerates from rest at first, then moves with constant velocity and finally decelerates uniformly to come to rest. If the ratio of the time taken is $1:8:1$ and the maximum speed attained is $60\text{km/h}$, then what is the average speed over the whole journey?

1. $48\text{km/h}$
2. $52\text{km/h}$
3. $54\text{km/h}$
4. $56\text{km/h}$

Q. A person travels along a straight road for the first half of the time with a velocity $v_1$ and the second half time with a velocity $v_2$. Then the mean velocity $\overline{v}$ is given by

1. $\overline{v}=\frac{v_1+v_2}{2}$
2. $\frac{2}{\overline{v}}=\frac{1}{v_1}+\frac{1}{v_2}$
3. $\overline{v}=\sqrt{v_1{v}_2}$
4. $\overline{v}=\sqrt{\frac{v_2}{v_1}}$

Q. An ant moves along the square loop of side $a\text{m}$. If it moves along path $ABC$, starting from $A$ to reach at the point $C$ in $2\text{s}$.

The average velocity of ant will be

1. Avergae velocity of ant is $a\text{m/s}$ along $ABC$
2. Avergae velocity of ant is $\frac{a}{\sqrt{2}}\text{m/s}$ along $AC$
3. Avergae velocity of ant is $\frac{3a}{\sqrt{2}}\text{m/s}$ along $BC$
4. Average velocity of ant is zero.

Q. The diagram shows the displacement-time graph for a particle moving in a straight line. The average velocity for the interval $t=0s$ to $t=5s$ is (Displacement is in $m$ and time is in $s$)

1. $0m{s}^{-1}$
2. $6m{s}^{-1}$
3. $-1m{s}^{-1}$
4. $-2m{s}^{-1}$

Q. A car runs at a constant speed on a circular track of radius $200\text{m}$, taking $62.8\text{s}$ on each lap. Find the average velocity and average speed for each complete lap.

1. $10\text{m/s}$ and $20\text{m/s}$
2. $0\text{m/s}$ and $20\text{m/s}$
3. $20\text{m/s}$ and $20\text{m/s}$
4. $0\text{m/s}$ and $10\text{m/s}$

Q. Find the average velocity of the position function $s\left(t\right)=2t^2-4t$ on the interval from $t=0\text{sec}$ to $t=5\text{sec}$.

1. $4\text{m/s}$
2. $5\text{m/s}$
3. $3\text{m/s}$
4. $6\text{m/s}$