Finding Average Velocity

Q. If a car covers $2/5^{th}$ of the total distance with $v_1$ speed and $3/5^{th}$ distance with $v_2$ speed then, average speed is

1. $\frac{2v_1{v}_2}{v_1+v_2}$
2. $\frac{5v_1{v}_2}{3v_1+2v_2}$
3. $\frac{1}{2}\sqrt{v_1{v}_2}$
4. $\frac{v_1+v_2}{2}$

Q.

Define distance, displacement, speed, velocity and acceleration.

Q. A car travels from $A$ to $B$ at a speed of $20\text{km/h}$ and returns at a speed of $30\text{km/h}$. The average speed of the car for the whole journey is

1. $25\text{km/h}$
2. $24\text{km/h}$
3. $50\text{km/h}$
4. $5\text{km/h}$

Q.

If a bullet of mass 5 gm moving with velocity 100 m/sec, penetrates the wooden block upto 6 cm. Then the average force imposed by the bullet on the block is

1. 417 N

2. 830 N

3. Zero

4. 8300 N

Q. A coin placed on a rotating turntable just slips if it is placed at a distance of $4cm$ from the center. If the angular velocity of the turntable is doubled, it will just slip at a distance of

1. $1cm$
2. $2cm$
3. $4cm$
4. $4cm$

Q.

A car starts from rest and accelerates uniformly for 10 sec to a velocity of 8 m/s.it then runs at a constant velocity and is finally brought to rest in 64 meters with a constant retardation. The total distance covered by the car is 584 meters. Find the value of acceleration, retardation and total time taken.

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.

At what temperature will the speed of sound be double of its value at $0^{\circ }C$ ?

Q.

One car moving on a straight road covers one-third of the distance with $20km.h{r}^{-1}$ and the rest with $60km.h{r}^{-1}$. The average speed is

1. $40km.h{r}^{-1}$

2. $80km.h{r}^{-1}$

3. $46\left(\frac{2}{3}\right)\mathrm{km}.h{r}^{-1}$

4. $36km.h{r}^{-1}$

Q.

A driver in a car, approaching a vertical wall, notices that the frequency of his car horn has changed from $440Hz$ to $480Hz$ when it gets reflected from the wall. If the speed of sound in air is $345m/s$, then the speed of the car is:

1. $24km/hr$

2. $36km/hr$

3. $54km/hr$

4. $18km/hr$

Q.

A car sounding its horn at $480Hz$ moves towards a high wall at a speed of $20m{s}^{-1}$. If the speed of sound is $340m{s}^{-1}$, the frequency of the reflected sound heard by the girl sitting in the car will be closest to?

1. $540Hz$

2. $524Hz$

3. $568Hz$

4. $480Hz$

Q.

A particle has an initial velocity $3\hat{i}+4\hat{j}$ and an acceleration of $0.4\hat{i}+0.3\hat{j}$. Its speed after $10s$ is

1. $10units$

2. $7units$

3. $7\sqrt{2}units$

4. $8.5units$

Q. A body covers half its journey in 40m/s and the other half with a speed of 60m/s . What is the average speed during the whole journey?

Q. A point traversed half of the distance with a velocity $v_0$. The remaining part of the distance was covered with velocity $v_1$ for half the time and with velocity $v_2$ for the other half of the time. The mean velocity of the point averaged over the whole time of motion is

1. $\frac{v_0+v_1+v_2}{3}$
2. $\frac{2v_0+v_1+v_2}{3}$
3. $\frac{v_0+2v_1+2v_2}{3}$
4. $\frac{2v_0(v_1+v_2)}{(2v_0+v_1+v_2)}$

Q. A body covers the first $\frac{1}{3}$ part of its journey with the speed of $2m/s$, next $\frac{1}{3}$ part with the speed of 3 m/s and the rest of the journey with a speed $6m/s$. The average speed of the body will be

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

Q. Distinguish between average speed and average velocity

Q. The displacement time graph of two moving particles make angles of ${30}^{\circ }$ and ${45}^{\circ }$ with the X- axis is shown. The ratio of their velocities is:

1. $\frac{\sqrt{3}}{2}$
2. $1$
3. $\frac{1}{2}$
4. $\frac{1}{\sqrt{3}}$

Q. The temperatures of two bodies measured by a thermometer are $t_1={20}^{\circ }C\pm {0.5}^{\circ }C$ and $t_2={50}^{\circ }C\pm {0.5}^{\circ }C$. The temperature difference and the error therein is:

1. ${70}^{\circ }C\pm {0.5}^{\circ }C$
2. ${30}^{\circ }C\pm 1^{\circ }C$
3. ${30}^{\circ }C\pm {0.5}^{\circ }C$
4. ${70}^{\circ }C\pm 1^{\circ }C$

Q. ​​​​​​A car moves at constant speed of 60km/hr for 1km and 40km/hr for next 1km. What is the average speed of the car?

Q. A car travel first $\frac{1}{3}rd$ of the total distance at $30\text{km/hr}$, next $\frac{1}{3}rd$ of the total distance at $40\text{km/hr}$ and last $\frac{1}{3}rd$ of the total distance at $24\text{km/hr}$. It's average speed in $\text{km/hr}$ for the whole Journey is

1. $30$
2. $28$
3. $40$
4. $35$

Q. A particle traversed half of the distance with a velocity $v_0$. The remaining part of the distance was covered with velocity $v_1$ for half the time and with velocity $v_2$ for the other half of the time. The mean velocity of the particle averaged over the whole time of motion is

1. $\frac{v_0+v_1+v_2}{3}$
2. $\frac{2v_0+v_1+v_2}{3}$
3. $\frac{v_0+2v_1+2v_2}{3}$
4. $\frac{2v_0(v_1+v_2)}{(2v_0+v_1+v_2)}$

Q.

A stone is thrown upwards from the top of a tower 85 m high . It reaches the ground in 5s . Calculate

1) the greatest height above the ground

2) the velocity with which it reaches the ground

3) the time taken to reach the maximum height.(g=10 m/ s^{​​​​​​2})

Q.

An aeroplane has to go from a point A to another point B, 500 km away due ${30}^0$ east of north. A wind is blowing due north at as speed of 20 m/s. The air-speed of the plane is 150 m/s.

(a) Find the directiion in which the pilot should head the plane to reach the point B.

(b) Find the time taken by the plane to go from A to B.

Q.

What is the rate of change of displacement called?

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.

Consider the situation of the previous problem. The man has to reach the other shore at the point, directly opposite to his starting point. If he reaches the other shore somewhere else, he has to walk down to this point. Find the minimum distance that he has to walk.

Q. A man walks on a straight road from his home to a market $2.5km$ away with a speed of $5km/h$. Finding the market closed, he instantly turns and walks back home with a speed of $7.5km/h$. The average speed of the man over the interval of time $0$ to $40$ minutes, is equal to

1. $5km/h$
2. $\frac{25}{4}km/h$
3. $\frac{30}{4}km/h$
4. $\frac{45}{8}km/h$

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

Q.

In the following example, try to identify the number of times the velocity of the ball changes: "A football player kicks a football to another player of his team who kicks the football towards the goal. The goalkeeper of the opposite team collects the football and kicks it towards a player of his own team". Also, identify the agent supplying the force in each case.

Q.

on turning a corner a car driver driving at 36 km per hour find the side on the road 55m ahead he immediately applies brakes so as to stop within 5 M of the child calculate the retardation produced and the time taken by the car to stop