Distance vs Displacement

Q.

The position of an object moving along the x-axis is given by $x=a+b{t}^2$, where $a=8.5\text{m}$ and $b=2.5\frac{\text{m}}{{\text{s}}^2}$, and t is measured in seconds. The average velocity of the object between t = 2s and t = 4s is

Q. Which of the following pairs of physical quantities does not have same dimensional formula?

1. Work and torque.
2. Impulse and linear momentum.
3. Angular momentum and Planck’s constant.
4. Tension and surface tension.

Q.

Give an example of each

1. Acceleration in the direction of motion.
2. Acceleration is against the direction of motion.
3. Acceleration is uniform.
4. Acceleration is non-uniform.

Q. A particle located at $x=0$ at time $t=0$, starts moving along the positive $x-$direction with a velocity $v$ that varies as $v=\alpha \sqrt{x}.$ The displacement of the particle varies with time as

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

Q. A bomb explodes in air when it has a horizontal speed of $10m/s$. It breaks into two pieces $A$ and $B$ of mass ratio $1:2$. If $A$ goes vertically up at a speed of $40m/s$, the speed of $B$ is

1. $20m/s$
   
2. $50m/s$
   
3. $30m/s$
   
4. $25m/s$
   

Q. An object has moved through a distance. Can it have 0 displacement? If yes, support your answer with examples.

Q. The location of a particle is changed. What can we say about the displacement and distance covered by the particle?

1. Both cannot be zero
2. Both must be zero
3. One of the two may be zero
4. Both must be equal

Q. The displacement of a particle moving in a straight line is described by the relation $x\text{(in m)}=6+12t-2t^2$. The distance covered by the particle in first $5\text{s}$ is

1. $16\text{m}$
2. $10\text{m}$
3. $24\text{m}$
4. $26\text{m}$

Q.

Two cars are moving in the same direction with the same speed $30\mathrm{km}/\mathrm{hr}$. They are separated by distance of $5\mathrm{km}$, the speed of a car moving in the opposite direction if it meets these two cars at an interval of $4\min$, will be

1. $40\mathrm{km}/\mathrm{hr}$

2. $45\mathrm{km}/\mathrm{hr}$

3. $30\mathrm{km}/\mathrm{hr}$

4. $15\mathrm{km}/\mathrm{hr}$

Q. Statement 1: Magnitude of average velocity is equal to average speed.
Statement 2: Magnitude of instantaneous velocity is equal to instantaneous speed.

1. Statement-1 is True; Statement-2 is True; Statement -2 is a correct explanation for Statement-1.
2. Statement-1 is True; Statement-2 is True; Statement -2 is NOT a correct explanation for Statement-1.
3. Statement-1 is True; Statement-2 is False.
4. Statement-1 is False; Statement-2 is True

Q. In a projectile motion, the velocity is perpendicular to acceleration at

1. no instance
2. one instant
3. all instants
4. two instants

Q. A body at rest breaks up into $3$ parts. If $2$ parts having equal masses fly off perpendicularly each after with a velocity of $12m/s$ then the velocity of the third part which has $3$ times mass of each part is

1. $6\sqrt{2}m/s$ at ${135}^{\circ }$ from each body
   
2. $4\sqrt{2}m/s$ at an angle of ${45}^{\circ }$ from each body
   
3. $4\sqrt{2}m/s$ at ${135}^{\circ }$ from each body
   
4. $24\sqrt{2}m/s$ at an angle of ${135}^{\circ }$ from each body
   

Q.

Is distance can be negative?

Q. A sphere rolls without slipping on a rough horizontal surface with centre of mass speed $v_0$. If mass of the sphere is $M$ and its radius is $R$, then what is the angular momentum of the sphere about the point of contact?

1. $\frac{5}{2}M{v}_{o}R$
2. $\frac{3}{5}M{v}_{o}R$
3. $\frac{7}{5}M{v}_{o}R$
4. $\frac{1}{2}M{v}_{o}R$

Q.

Give SI unit of distance and displacement.

Q.

The SI unit of displacement is

Q.

Under what condition will the displacement and distance of a moving object has the same magnitude ?

Q. A ship A is moving towards west with a speed of 10 km/h and another ship B, which is 100 km south of A, is moving northwards with a speed of 10 km/h. Find the time after which the distance between them becomes shortest.

Q. A particle is projected horizontally from the top of a tower with a velocity. If ${\upsilon }_0$ be its velocity at any instant, then the radius of curvature of the path of the particle at that instant is directly proportional to

1. ${\text{v}}^2$
2. $\frac{1}{\text{v}}$
3. $\text{v}$
4. ${\text{v}}^3$

Q. An aircraft executes a horizontal loop of radius $1.00\text{km}$ with a steady speed of $900\text{km/h}$. Compare its centripetal acceleration with the acceleration due to gravity.

Q. In the figure shown, both the blocks are released from rest. The time (in $s$) to cross each other is

Q. A metal coin of mass \(5~g\) and radius 1 \(~cm\) is fixed to a thin stick \(AB\) of negligible mass as shown in the figure. The system is initially at rest. The constant torque, that will make the system rotate about \(AB\) at \(25\) rotations per second in \(5~s\), is close to

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 body of mass $2kg$ lying on a smooth surface is attached to a string $3m$ long and then whirled round in a horizontal circle making $60$ revolution per minute. The centripetal acceleration will be

1. $1.18m/s^2$
2. $118.4m/s^2$
3. $2.368m/s^2$
4. $23.68m/s^2$

Q.

In what condition the distance covered is equal to the magnitude of the displacement of the particle?

Q.

A stone is thrown vertically upwards and after ascending height h it comes back to the hands of the thrower. Calculate the net displacement of the stone?

Q. Five persons $A,B,C,D$ and $E$ are pulling a cart of mass $100kg$ on a smooth surface and cart is moving with acceleration $3m/s^2$ in east direction. When person 𝐴 stops pulling, it moves with acceleration $1m/s^2$ in the west direction. When person $B$ stops pulling, it moves with acceleration $24m/s^2$ in the north direction. The magnitude of acceleration (in $m/s^2$) of the cart when only $A$ and $B$ pull the cart keeping their directions same as the old directions, is:

Q.

An object moves from A to D through B and C along a rectangular path as shown in the figure. Find:
(A) the distance covered by the object.
(B) the displacement of the object.

Q.

When a particle moves in a straight line from point A to point B the distance covered is ___ the magnitude of the displacement.

Q.

Why does an apple from an apple tree falls on earth but not on the moon?