Direction of Instantaneous Velocity

Q.

Two trains each 50m long are travelling in opposite direction with velocity 10m/s and 15m/s. The time of crossing is..

Q. In the given arrangement of a charged square frame find electric field at centre. The linear charge density is as shown in figure.

1. $\frac{\lambda \sqrt{2}}{4\pi {ϵ}_{0}l}[-2i+14j]$
2. $\frac{\lambda \sqrt{2}}{4\pi {ϵ}_{0}l}[-2i+14j]$
3. Zero
4. None of these

Q. Two masses m1 and m2 are placed at a separation r. Find out the moment of inertia of the system about an axis passing through its centre of mass and perpendicular to the line joining the masses.

Q.

a train is moving towards east with a speed of 20m/s . A person is running on the roof of the train with a speed 3m/s against the motion of train . Velocity of the person as seen by an observer on ground will be-

Ans is 17m/s towards east..how?

Q.

Obtain the expression of relative velocity

Q.

A particle starts from a point A and travels along the sold curve shown in figure. Find approximaterly the position B of the particle such that the average velocity between the position A and B has the same direction as the instantaneous velocity at B

Q. A heavy particle is projected with a velocity at an angle with the horizontal into a uniform gravitational field. The slope of the trajectory of the particle varies not according to which of the following curve?

1. 
2. 
3. 
4. 

Q.

Suppose the platform with the kid in the previous problem is rotating in anticlockwise direction at an angular speed $\omega$. The kid starts walking along the rim with a speed v relative to the platform also in the anticlockwise direction. Find the new angular speed of the platform.

Q.

Two cars A and B are moving in same direction with a speed of 30km per hr. They are separated from each other by 5 km. Third car moving in the opposite direction meets the two cars after an interval of 4 mins. The speed of third car is ? ( use relative velocity to solve the problem)

1. 30km per hr

2. 25km per hr

3. 40km per hr

4. 45km per hr

Q.

A car travels equal distances in the same direction with velocities of $60km/h,20km/h,and10km/h$ respectively. The average velocity of the car over the whole journey is

1. 5m/s

2. 6m/s

3. 7m/s

4. 8m/s

Q. In the figure shown if friction co-efficient of block $1$ and $2$ with inclined plane is ${\mu }_1=0.5$ and ${\mu }_2=0.4$ respectively, then find out the correct statement.

1. there is a non-zero contact force between two blocks.
2. both blocks will move sepeartely
3. both blocks will move together
4. none of these

Q.

If, in Exercise 5.21, the speed of the stone is increased beyond the maximum permissible value, and the string breaks suddenly, which of the following correctly describes the trajectory of the stone after the string breaks:
a) the stone moves radially outwards,
b) the stone flies off tangentially from the instant the string breaks,
c) the stone flies off at an angle with the tangent whose magnitude depends on the speed of the particle ?

Q. The radii of the front and the hind wheels of a carriage are a and b respectively;c is the distance between the axes.A particle of mud driven from the highest point of the hind wheel is observed to alight on the highest point of the front wheel.Show that the velocity of the carriage is [g(c+b-a)(c+a-b)/{4(b-a)}]^(1/2)

Q.

A clock has a minute hand of length 14 cm. At what speed does the tip of the minute hand move in a duration of half an hour?

1. $\frac{7}{450}$$cm{s}^{-1}$

2. $\frac{11}{450}cm{s}^{-1}$

3. $\frac{44}{450}$$cm{s}^{-1}$

4. $\frac{16}{750}$$cm{s}^{-1}$

Q.

A particle moves along a circle of radius $10m$. Determine the distance and magnitude of displacement after
(a) $0.5$ revolution
(b) $2$ revolutions
(c) $2.5$ revolutions

Q. A bird is flying towards north with a velocity $40\text{km/h}$ and a train is moving with a velocity $40\text{km/h}$ towards east. What is the velocity of the bird noted by a man in the train ?

1. $40\sqrt{2}\text{km/h N-E}$
2. $40\sqrt{2}\text{km/h S-E}$
3. $40\sqrt{2}\text{km/h N-W}$
4. $40\sqrt{2}\text{km/h S-W}$

Q.

A bus moves with uniform velocity along a straight-line path. If the average velocity of the bus is $80km{h}^{-1}$ then its instantaneous velocity at $t=0$ is _______ $km{h}^{-1}$.

1. 70

2. 100

3. 80

4. zero

Q.

What is speed?

Q.

What do you understand by the given statement: The path length covered by a body is zero?

Q. Two trains $\text{A}$ and $\text{B}$ have lengths $800\text{m}$ and $1000\text{m}$ respectively and are moving with the velocity of $25\text{m/s}$ and $15\text{m/s}$ respectively in the same direction. At time $t=0$ engine of train $\text{A}$ is just behind train $\text{B}$. Find time when train $\text{A}$ completely overtakes train $\text{B}$?

1. $10\text{sec}$
2. $36\text{sec}$
3. $18\text{sec}$
4. $180\text{sec}$

Q. If the force on a rocket is $400\text{N}$ and relative velocity of mass emission is $500\text{m/s}$, then the rate of combustion of the fuel will be

1. $0.8\text{kg/s}$
2. $0.6\text{kg/s}$
3. $0.4\text{kg/s}$
4. $0.2\text{kg/s}$

Q. Why is it dangerous to jump out of a moving bus?

Q. A bus travels the first one third distance at a speed of $10km{h}^{-1}$, the next one third distance at a speed of $20km{h}^{-1}$ and the next one third distance at a speed of $30km{h}^{-1}$ .

1. $20{ms}^{-1}$
2. $\frac{50}{11}{ms}^{-1}$
3. $\frac{180}{11}{ms}^{-1}$
4. $30{ms}^{-1}$

Q. Why is it advised to tie any luggage kept on the roof of a bus with rope?

Q.

The position vector $\overrightarrow{r}=5.00t\hat{i}+(et+f{t}^2)\hat{j}$ locates a particle as a function of time t. Vector $\overrightarrow{r}$ is in meters, t is in seconds, and factors e and f are constants. Below Diagram gives the angle $\theta$ of the particle's direction of travel as a function of t($\theta$) is measured from the positive x direction). What are 'e' and 'f', including units?

1. $e=\frac{35}{6\sqrt{3}}m/s,f=\frac{-5}{24\sqrt{3}}m/s^2$

2. $e=\frac{-35}{6\sqrt{3}}m/s,f=\frac{5}{24\sqrt{3}}m/s$

3. $e=\frac{35}{6\sqrt{3}}m/s,f=\frac{5}{24\sqrt{3}}m/s^2$

4. $e=\frac{35}{6\sqrt{3}}m/s,f=\frac{5}{24\sqrt{3}}m/s^2$

Q. If a force of constant magnitude acts in direction perpendicular to the motion of a particle, then its

1. Speed is uniform
2. Momentum is uniform
3. Velocity is uniform
4. All of these

Q. When a particle moves with constant velocity its average velocity, its instantaneous velocity and its speed all are equal. Is this statement true or false?

1. True
2. False

Q. The position of particle along $x$ axis is given by $x=t^2-5t+6$, where $x$ is in meters & $t$ is in seconds. The distance covered in first 3 seconds is

1. 6.0 m
2. 8.0 m
3. 6.5 m
4. 7.0 m

Q. A position–time graph for a particle moving along the $x$ axis is shown in above figure. (a) Find the average velocity in the time interval $t=1.50s$ to $t=4.00s$. (b) Determine the instantaneous velocity at $t=2.00s$ by measuring the slope of the tangent line shown in the graph. (c) At what value of $t$ is the velocity zero.

Q. A 120m long train is moving in a direction with speed 20m/s. A train B moving with 30 m/s in the opposite direction and 130 m long crosses the first train in a time

1. 38 s
2. None of these
3. 6 s
4. 36 s