Average velocity

Q. A car accelerated from initial position and then returned at initial point, then

1. average velocity is zero but average speed is non-zero.
2. average speed is zero but average velocity is non-zero.
3. both speed and velocity has non zero average.
4. both speed and velocity has zero average.

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.

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

1. $80/3m{s}^{-1}$
2. $40m{s}^{-1}$
3. $25m{s}^{-1}$
4. $30m{s}^{-1}$

Q.

A particle moves along the sides AB, BC, and CD of a square of side 25 m with a speed of 15. Its average velocity is________.

1. 15 m/s

2. 10 m/s

3. 7.5 m/s

4. 5 m/s

Q. Mr. Sharma goes for jogging every morning in a circular park whose circumference is $1\text{km}$. He makes $3$ complete circles in $50\text{minutes}$. Find his average velocity.

1. $10\text{m/s}$
2. $10\text{km/s}$
3. $8.2\text{km/s}$
4. $0\text{m/s}$

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. The velocity of a particle is $v=v_0+gt+f{t}^2$. If its position is $x=0$ at $t=0$, then its displacement after unit time $(t=1)$ is

1. $v_0+g/2+f$
2. $v_0+2g+3f$
3. $v_0+g/2+f/3$
4. $v_0+g/2+2f$

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 $\text{m/s}$) and average speed(in $\text{m/s}$) respectively in each lap.

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

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. 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. The position of a particle along x-axis at time $t$ is given by $x=1+t-t^2\text{m}$. The distance travelled by the particle in first $2\text{sec}$ is

1. $1\text{m}$
2. $2\text{m}$
3. $2.5\text{m}$
4. $3\text{m}$

Q. A drunk person moves such that after three consecutive steps forward he takes one step backwards. There is a ditch 10 m away from him when he starts moving in its direction. If his each step is 1 m long and he takes 1 sec to take each step, his average velocity till he falls in ditch is [step in which he falls should not be counted]

1. $\frac{10}{17}$ m/s
2. $\frac{1}{2}$ m/s
3. $1$ m/s
4. $\frac{5}{9}$ 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. A body traveling along a straight line traversed first 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 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. 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. 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 particle moves along a semicircle of radius $10\text{m}$ in 5 seconds. The average velocity of the particle is

1. $2\pi m{s}^{-1}$
2. $4\pi m{s}^{-1}$
3. $2m{s}^{-1}$
4. $4m{s}^{-1}$

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. Mr. Sharma goes for jogging every morning in a circular park whose circumference is $1\text{km}$. He makes $3$ complete circles in $50\text{minutes}$. Find his average velocity.

1. $10\text{m/s}$
2. $10\text{km/s}$
3. $8.2\text{km/s}$
4. $0\text{m/s}$

Q. Find the average velocity of the position function $s\left(t\right)=3t^2-6t$ on the interval from $t=0\text{sec}$ to $t=4\text{sec}$.

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

Q.

The graph represents the s-t curve of a body moving in a straight line. At which moment 't' is the instantaneous velocity approximately equal to the average velocity over the first 't' seconds?

1. $t=t_1$

2. $t=t_2$

3. $t=t_3$

4. $t=t_4$

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. 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. A drunk person moves such that after three consecutive steps forward he takes one step backwards. There is a ditch 10 m away from him when he starts moving in its direction. If his each step is 1 m long and he takes 1 sec to take each step, his average velocity till he falls in ditch is [step in which he falls should not be counted]

1. $\frac{10}{17}$ m/s
2. $\frac{1}{2}$ m/s
3. $1$ m/s
4. $\frac{5}{9}$ m/s

Q. A cyclist starting from point $A$ travels $200m$ due north to a point $B$ at a constant speed of $5m/s$. He rests at $B$ for $30sec$ and then travels $300m$ due south to a point $C$ at a constant speed of $10m/s$. Find the average velocity. Take north as positive.

1. $1m/s$
2. $-1m/s$
3. $2m/s$
4. $-2m/s$

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 body moves from A to B in 3 sec. What is its average velocity w.r.t. the origin?

1. 35 m/s

2. 10 m/s

3. -35 m/s

4. -10 m/s

Q.

What is the average velocity of the coin?

1. 1 m/sec

2. $\frac{5}{3}m/sec$

3. -1m/sec

4. -10m/sec

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

1. $80/3m{s}^{-1}$
2. $40m{s}^{-1}$
3. $25m{s}^{-1}$
4. $30m{s}^{-1}$