Average velocity

Q. A body travels the first half of the total distance with velocity $v_1$ and the second half with velocity $v_2$. Calculate the average velocity.

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

Q. The $v-t$ plot of a moving object is shown in the figure. The average velocity of the object during the first $10\text{seconds}$ is

1. $0$
2. $2.5\text{ms}$
3. $5\text{ms}$
4. $2\text{ms}$

Q.

The magnitude of average velocity is always equal to the average speed.

1. True
2. False

Q. A body travelling along a straight line traversed one third of the total distance with a velocity $4\text{m/s}$. The remaining part of the distance was covered with a velocity $2\text{m/s}$ for half the time and with velocity $6\text{m/s}$ for the other half of time. The mean velocity averaged over the whole time of motion is

1. $5\text{m/s}$
2. $4\text{m/s}$
3. $4.5\text{m/s}$
4. $3.5\text{m/s}$

Q. A table clock has its minute hand $4cm$ long. Find the average velocity of the tip of the minute hand (a) between 6 AM to 6:30 AM and (b) between 6 AM to 6:30 PM

1. $4\times {10}^{-3}\frac{cm}{s},1.8\times {10}^{-4}\frac{cm}{s}$
2. $4.4\times {10}^{-3}\frac{cm}{s},1.8\times {10}^{-4}\frac{cm}{s}$
3. $0.44\times {10}^{-3}\frac{cm}{s},1.8\times {10}^{-4}\frac{cm}{s}$
4. $4.4\times {10}^{-3}\frac{cm}{s},0.18\times {10}^{-4}\frac{cm}{s}$

Q.

When the magnitude of average velocity is the same as that of average speed?

Q.

A body is moving in a straight path. Then,

1. its instantaneous speed is equal to its instantaneous velocity.

2. its average speed is equal to its average velocity.

3. its acceleration is equal to a change in its velocity.

4. Both (a) and (b).

Q. The figure shows the graph of the $x-$coordinate of a particle moving along the $x-$axis as a function of time. Average velocity during $t=0$ to $t=6\text{s}$ is

1. $10\text{m/s}$
2. $60\text{m/s}$
3. $5\text{m/s}$
4. $0$

Q. A body moves in straight line with velocity $v_1$ for ${\left(\frac{1}{3}\right)}^{rd}$ of time and for remaining time with $v_2$. Find the average velocity of body.

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

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 train accelerating uniformly from rest attains a maximum speed of $40{\text{ms}}^{-1}$ in $20\text{s}$. It travels at this speed for $20\text{s}$ and is brought to rest by uniform retardation in further $40\text{s}$. What is the magnitude average velocity during this period?

1. $80/3{\text{ms}}^{-1}$
2. $40{\text{ms}}^{-1}$
3. $25{\text{ms}}^{-1}$
4. $30{\text{ms}}^{-1}$

Q.

Will the average speed be greater than average velocity?

1. Yes

2. No

Q.

Under what condition(s) is the magnitude of the average velocity of an object equal to its average speed?

Q. The position $x$ of a moving particle at time $t$ is given by $x=t^2+2t+3\text{m}$. The average velocity of the particle during the first second of its motion is

1. $1{\text{ms}}^{-1}$
2. $2{\text{ms}}^{-1}$
3. $3{\text{ms}}^{-1}$
4. $4{\text{ms}}^{-1}$

Q. If a particle has velocity $v\left(t\right)=18-6t\text{m/s}$, the magnitude of average velocity in $10\text{sec}$ is

1. $-10\text{m/s}$
2. $12\text{m/s}$
3. $10\text{m/s}$
4. $-8\text{m/s}$

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(in $m/s$) and average speed(in $m/s$) respectively in each lap.

1. 20 and zero
2. 0 and 20
3. 20 and 20
4. 6.3 and 20

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(in $m/s$) and average speed(in $m/s$) respectively in each lap.

1. 20 and zero
2. 0 and 20
3. 20 and 20
4. 6.3 and 20

Q.

A body traveling along a straight line traversed one third of the total distance with a velocity 4 m/s. The remaining part of the distance was covered with a velocity 2 m/s for half of the time and with velocity 4 m/s for the other half of time. The mean velocity averaged over the whole time of motion is

1. 5

2. 4

3. 0

4. 2

Q. A bus is going from Delhi to Lucknow via different routes $A\&B$ respectively as shown in the figure. If bus takes $6\text{hrs}$ via route $A$ and $8\text{hrs}$ via route $B$. Then find the average velocity of the bus via route $B$

1. $70\text{km/hr}$
   
2. $60\text{km/hr}$
3. $110\text{km/hr}$
4. $40\text{km/hr}$

Q.

The position of an elevator varies with time according to the function $x\left(t\right)=t^2+2t+3$

Find the
$\left(1\right)$ average velocity between time interval $t=0\text{s}$ to $t=2\text{s}$.
$\left(2\right)$ instantaneous velocity of the elevator at time $t=3\text{s}$.

1. $v_{avg}=8\text{m/s}$ ; $v_{ins}=11\text{m/s}$
2. $v_{avg}=4\text{m/s}$ ; $v_{ins}=8\text{m/s}$
3. $v_{avg}=8\text{m/s}$ ; $v_{ins}=4\text{m/s}$
4. $v_{avg}=11\text{m/s}$ ; $v_{ins}=4\text{m/s}$

Q. If a particle is moving from its initial position $x=-5\text{m}$ to a position $x=-11\text{m}$ in $2\text{s}$ along a straight line. What will be the average velocity of particle ?

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

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. The position of a particle moving along x-axis is given by $x=(5t^2-4t+20)\text{m}$, where $t$ is in second. Find the magnitude average velocity between $1\text{s}$ and $3\text{s}$.

1. $10\text{m/.s}$
2. $16\text{m/.s}$
3. $14\text{m/.s}$
4. $5\text{m/.s}$

Q. If a particle has velocity $v\left(t\right)=t^2-5t+6$, the average velocity in $5\text{sec}$ is

1. $\frac{13}{14}\text{m/s}$
2. $\frac{14}{15}\text{m/s}$
3. $\frac{11}{12}\text{m/s}$
4. $\frac{7}{9}\text{m/s}$

Q.

The position of an elevator varies with time according to the function $x\left(t\right)=t^2+2t+3$

Find the
$\left(1\right)$ average velocity between time interval $t=0\text{s}$ to $t=2\text{s}$.
$\left(2\right)$ instantaneous velocity of the elevator at time $t=3\text{s}$.

1. $v_{avg}=8\text{m/s}$ ; $v_{ins}=11\text{m/s}$
2. $v_{avg}=4\text{m/s}$ ; $v_{ins}=8\text{m/s}$
3. $v_{avg}=8\text{m/s}$ ; $v_{ins}=4\text{m/s}$
4. $v_{avg}=11\text{m/s}$ ; $v_{ins}=4\text{m/s}$

Q. A particle moves along a straight line and its velocity depends on time as $v=4t-t^2.$Then for first $5\text{sec}$

1. average velocity is $\frac{25}{3}\text{m/s}$
2. average velocity is $10\text{m/s}$
3. average velocity is $\frac{5}{3}\text{m/s}$
4. average velocity is $\frac{13}{5}\text{m/s}$

Q. If a particle has velocity $v\left(t\right)=18-6t\text{m/s}$, the magnitude of average velocity in $10\text{sec}$ is

1. $-10\text{m/s}$
2. $12\text{m/s}$
3. $10\text{m/s}$
4. $-8\text{m/s}$

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. Magnitude of average velocity of a particle moving in a straight line, with constant acceleration $a$ and initial velocity $u$ in first $t$ seconds is

1. $u+\frac{1}{2}at$
2. $u+at$
3. $\frac{u+at}{2}$
4. $\frac{u}{2}$