Displacement

Q. At t=0, an aeroplane which is vertically above a ground observer is going towards east at a speed of $510km/h$ at a height of $2000m$. At a certain instant, the sound of the plane heard by the ground observer appears to come from a point vertically above him. How far is the plane at this instant from where it was at t=0? Speed of the sound in air $=340m/s$.

1. $633m$
2. $733m$
3. $833m$
4. $933m$
   

Q.

The numerical ratio of displacement to distance of a moving object is :

1. Always less than unity

2. Always equal to 1

3. Always more than 1

4. Equal or less than 1.

Q. A Body moves 6 m north. 8 m east and 10m vertically upwards, what is the magnitude of its resultant displacement from initial position?

1. $10\sqrt{2}m$
2. $10m$
3. $\frac{10}{\sqrt{2}}m$
4. $10\times 2m$

Q. A boat in the river accelerates in a straight line starting from rest at a constant rate of $3{\text{m/s}}^2$ for $10\text{s}$. How far does the boat travel during this time ?

1. $96\text{m}$
2. $104\text{m}$
3. $150\text{m}$
4. $76\text{m}$

Q. Displacement of the particle in a closed loop is

1. always zero.
2. greater than the distance covered.
3. equal to the distance covered.
4. infinite.

Q. Distance and displacement are always positive.

1. False
2. True

Q. At t=0, an aeroplane which is vertically above a ground observer is going towards east at a speed of $510km/h$ at a height of $2000m$. At a certain instant, the sound of the plane heard by the ground observer appears to come from a point vertically above him. How far is the plane at this instant from where it was at t=0? Speed of the sound in air $=340m/s$.

1. $633m$
2. $733m$
3. $833m$
4. $933m$
   

Q.

A car runs at a constant speed on a circular track of radius 300 m, taking time 62.8 seconds on each lap. Calculate the average speed and average velocity on each lap.

Q. A hall has the dimensions $10m\times 10m\times 10m.$ A fly starting at one corner ends up at a diagonally opposite corner. The magnitude of its displacement is nearly

1. $5\sqrt{3}m$
2. $10\sqrt{3}m$
3. $20\sqrt{3}m$
4. $30\sqrt{3}m$

Q. A car accelerates from rest at a constant rate $\alpha$ for some time, after which it decelerates at a constant rate $\beta$ and finally come to rest. If the total time elapsed is $t$ seconds, the total distance travelled is -

1. $\frac{\alpha \beta }{2(\alpha +\beta )}{t}^2$
2. $\frac{\alpha \beta }{4(\alpha +\beta )}{t}^2$
3. $\frac{4\alpha \beta }{(\alpha +\beta )}{t}^2$
4. $\frac{2\alpha \beta }{(\alpha +\beta )}{t}^2$

Q.

The numerical ratio of displacement to distance for a moving object is.

1. always less than 1

2. always equal to 1

3. always more than 1

4. equal or less than 1

Q.

In a journey, numerical value of $displacement\le dis\tan ce$.

1. True
2. False

Q. The magnitude of displacement can be zero even when the distance is non zero.

1. False
2. True

Q. A man goes $10\text{m}$ towards North, then $20\text{m}$ towards east. Then, total length of displacement is

1. $22.4\text{m}$
2. $25\text{m}$
3. $25.5\text{m}$
4. $30\text{m}$

Q. A wheel of radius 1 meter rolls forward half a revolution on a horizontal ground. The magnitude of the displacement of the point of the wheel initially in contact with the ground is

1. $2\pi$
2. $\sqrt{2}\pi$
3. $\sqrt{{\pi }^2+4}$
4. $\pi$

Q. An athlete finishes a round circular track of radius $R$ in $40\text{s}$. What is the displacement at the end of $2\text{minutes 20 s}$?

1. $\text{2R}$
2. $\text{2πR}$
3. $\text{7πR}$
4. Zero

Q. A particle moving with an initial velocity of $10\text{m/s}$ on a straight path is subjected to a uniform acceleration of $-5{\text{m/s}}^2$. Find the displacement in the next $4\text{s}$.

1. $80\text{m}$
2. $40\text{m}$
3. $20\text{m}$
4. Zero

Q. Displacement of the particle in a close loop is

1. always zero.
2. greater than the distance covered.
3. equal to the distance covered.
4. infinite.

Q. A body is moving unidirectionally under the influence of a source of constant power, its displacement in time $t$ is proportional to

1. $t^{1/2}$
2. $t$
3. $t^{3/2}$
4. $t^2$

Q. The velocity of a particle is $v=v_0+ct+g{t}^2$. If its position is $x=0$ at $t=0$, then its displacement at time $(t=2\text{sec})$ is

1. $2v_0+2c+\frac{8g}{3}$
2. $2v_0+c+\frac{g}{3}$
3. $2v_0+2c+\frac{2g}{3}$
4. $2v_0+2c+\frac{6g}{3}$

Q. Which of the following expression correctly represents displacement of a particle ?

1. Initial Position - Final Position
2. -Initial Position + Final Position
3. Initial Position + Final Position
4. -Initial Position - Final Position

Q. The displacement of tip of the second hand of an analog watch when it turns for $15\text{sec}$ is

1. $5\text{cm}$
2. $10\text{cm}$
3. $5\sqrt{2}\text{cm}$
4. $3\sqrt{2}\text{cm}$

Q. A man of mass $50\text{kg}$ is in a lift at ground floor. The man is now on a weight machine. For first $10\text{s}$, reading of weighing machine is $60\text{kg-wt}$. For next $10\text{s}$, it reads $50\text{kg-wt}$ and for rest of the journey till top floor, reading of weighing machine is $30\text{kg-wt}$. Assume that initial and final velocity of lift is zero. Total distance travelled by the lift is $50x\text{m}$. The value of $x$ is _______.

$(g=10{\text{m/s}}^2)$

Q. Consider two particles $P$ and $Q$. Particle $P$ moves from $A$ to $B$ and particle $Q$ moves from $C$ to $D$. If the displacement of particle $P$ and $Q$ be $x$, $y$ respectively. Then:

1. $x=y$
2. $x<y$
3. $x>y$
4. $x\ge y$

Q.

The numerical ratio of displacement to distance for a moving object is:

1. Always less than 1

2. Always equal to 1

3. Always more than 1

4. Equal or less than 1

Q. John travels $250\text{m}$ to North but then back-tracks to South for $100\text{m}$ to pick up a friend. What is John’s total displacement?

1. $100\text{m}$
2. $150\text{m}$
3. $50\text{m}$
4. $250\text{m}$

Q. A particle is moving with a velocity of $v=(3+6t+9t^2)\text{cm}/s$. Find out the displacement of the particle in the interval $t=5\text{s}$ to $t=8\text{s}$.

1. $1280\text{cm}$
2. $1287\text{cm}$
3. $1285\text{cm}$
4. $1280\text{cm}$

Q. A drunkard takes a step of $1\text{m}$ in 1 second. He takes 5 steps forward and 3 steps backwards, and so on. The time taken by him to fall in a pit $13\text{m}$ away from the starts is

1. 26 seconds
2. 31 seconds
3. 37 seconds
4. 41 seconds

Q. A force $\overrightarrow{F}=-k(y\hat{i}+x\hat{j})$, where $k$ is a constant, acts on a particle moving in the x-y plane. Starting from the origin, the particle is taken from the origin $(0,0)$ to the point $(a,0)$ and then from the point $(a,0)$ to the point $(a,a)$. The total work done by the force $\overrightarrow{F}$ on the particle is

1. $k{a}^2$
2. $-k{a}^2$
3. $2k{a}^2$
4. $-2k{a}^2$

Q. A car travels $6\text{km}$ towards the north at an angle ${45}^{\circ }$ to the East and then travels distance of $4\text{km}$ towards the north at an angle ${135}^{\circ }$ to the east. How far is the point from the starting point ? What angle does the straight line joining its initial and final positions, makes with the east ?

1. $\sqrt{50}\text{km}$ and $ta{n}^{-1}\left(5\right)$
2. $\sqrt{10}\text{km}$ and $ta{n}^{-1}\left(\sqrt{5}\right)$
3. $\sqrt{52}\text{km}$ and $ta{n}^{-1}\left(5\right)$
4. $\sqrt{52}\text{km}$ and $ta{n}^{-1}\left(\sqrt{5}\right)$