Distance vs Displacement

Q. For a particle undergoing rectilinear motion with uniform acceleration, the magnitude of displacement is one third the dis†an ce covered in some time interval. The magnitude of final velocity is less than magnitude of initial velocity for this time interval. Then the ratio of initial speed to the final speed for this time interval is : (A) V2 (B) 2 (C) 73 (D) 3​

Q.

A plot of potential energy and kinetic energy versus displacement x for a block attached to a spring obeying Hooke's law is

1. a hyperbola

2. a straight line

3. a parabola

4. an ellipse

Q. 46. What is rise in temp of a coolective drop when initially 1 gm and 2 gm drops travel with velocities 10 cm/sec and 15cm/sec?

Q. Two particles of equal mass m are moving round a circle of radius r due to their mutual gravitational interaction . Find time period of each particle.

Q. 64.What is the relationship between simple harmonic motion and uniform circular motion?

Q. A person can run on ground with a maximum speed of 6 m/s. The person stands on the rear end of roof atrain moving with constant velocity. The length of train is 120 m. The man begins to run at this maximum acapacity towards the front end, reaches the front end, immediately -turns back and run towards the rear end.Finci the net displacement of the man wir.t. ground by the time he reaches back to rear end. The velocity of train is 10 m/s 1)0 2) 400 m (3) 100 m (4)200 m

Q. 1.A particle of mass m is released from rest and follows a parabolic path as shown Assuming that the displacement of mass from the origin is small Find equational relation between position and time. Also show position time graph

Q. a wheel rotating with angular speed w0 is suddenly switched off.The angular retardation is directly propotional to the angular speed at any instant, the constant being k . Find angular speed as function of time

Q. The projection of uniform circular motion on any chord (except diameter) is simple harmonic motion or not?

Q. Three identical bodies each of mass M are placed at vertices of an equilateral triangle of arm L keeping the triangle as such by which speed bodies should be rotated in their gravitational fields so that the particle moves along the circumference of circular orbit

Q.

What will be the speed of center of mass, if a solid sphere of radius 20 cm which rotates at 2 rps along a straight line?

1. 2.51 m/s

2. 2.55 m/s

3. 2.22 m/s

4. 2.50 m/s

Q. The position of a particle moving in a straight line is described by the relation $x=3+6t-t^2\text{m}$. The distance covered by the particle in metres in first $6\text{s}$ is

Q. A particle A placed at origin at t = 0 moves with constant velocity of 2 m/s. Another particle B placed at (3 m, 4 m) at t = 0 moves with constant velocity of (2ỉ --j )m/s. Particle A has its direction so as to reach as closest as possible to particle B. If Va is velocity of A and Rmin is the distance of closest approach, then show that angle theta should be zero for closest approach.

Q. Three identical bodiee of equal mass M each are moving along a circle of radius R under the action of their mutual gravitational attraction. the speed of each body is

Q. A car travels with the speed of $15\text{m/s}$ for $0<t\le 10\text{sec}$, $20\text{m/s}$ for $10<t\le 20\text{sec}$ and $5\text{m/s}$ for $20<t\le 25\text{sec}$. The total distance travelled by the car is

1. $175\text{m}$
2. $375\text{m}$
3. $275\text{m}$
4. $300\text{m}$

Q.

An ant moves from A to B then to C. The distance 'd' and displacement 's' of the ant is cm and cm respectively?

1. 7
2. 3
3. 5
4. 8

Q. Explain clearly, with examples, the distinction between : (a) magnitude of displacement (sometimes called distance) over an interval of time, and the total length of path covered by a particle over the same interval; (b) magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval]. Show in both (a) and (b) that the second quantity is either greater than or equal to the first. When is the equality sign true ? [For simplicity, consider one-dimensional motion only].

Q. Two particles $1$ and $2$ are moving with constant velocities ${\overrightarrow{v}}_1=4\hat{i}-3\hat{j}\text{m/s}$ and ${\overrightarrow{v}}_2=b\hat{i}-\hat{j}\text{m/s}$ respectively. The position vectors of the particles at time $t=0$ are ${\overrightarrow{r}}_1=5\hat{i}+2\hat{j}\text{m}$ and ${\overrightarrow{r}}_2=-4\hat{i}-4\hat{j}\text{m}$. If they collide, which of the following is correct. ($b$ is a constant)

1. They collide at $t=3\text{sec}$
2. Their time of collision cannot be found
3. $b=7$
4. $b=-1$

Q. 79.Find u, length of AB, velocity at B

Q. Statement 1: A body is moving along a straight line such that its velocity varies with time as shown in figure. Magnitude of displacement of the body from $t=0$ to $t=12$ s is the same as the distance travelled by it in the given time duration.


Statement 2: For unidirectional motion of a body, |displacement|=distance.

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. A particle is rotated in a vertical circle by connecting it to a string of length l and keeping the other end of the string fixed the minimum speed of the particle when the string is horizontal for which the particle will complete the circle is

Q. The numerical ratio of displacement to distace for 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. 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.

The ratio of the numerical values of the average velocity and average speed of a body is always

1. Unity or less

2. Unity or more

3. Less than unity

4. Unity

Q. A car travels with the speed of $15\text{m/s}$ for $0<t\le 5\text{sec}$, $20\text{m/s}$ for $5<t\le 10\text{sec}$ and $5\text{m/s}$ for $10<t\le 15\text{sec}$. The total distance travelled by the car is

1. $250\text{m}$
2. $100\text{m}$
3. $200\text{m}$
4. $150\text{m}$

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 body is moving with uniform retardation covers 3km before its speed is reduced to half of its initial value it comes to rest in another distance of

Q. Which of the following decreases in motion along a straight line with constant retardation while the body is moving away from the origin?

1. Mass
2. Speed
3. Displacement
4. None of the above

Q.

A body is moving along the curve $ABC$ as shown in the figure and the initial and final positions are $A$ and $C$, respectively. Displacement is the line joining

1. initial and final position of the body.

2. midpoint $\left(B\right)$ and final position of the body.

3. midpoint $\left(C\right)$ and final position of the body.

4. Both $\left(B\right)$ and $\left(C\right)$

Q. Let $\underset{A}{\to }$ be a unit vector along the axis of rotation of a purely rotating body and $\underset{B}{\to }$ be a unit vector along the velocity of a particle P of the body away from the axis. The value of $\underset{A}{\to }.\underset{B}{\to }$ is
(a) 1
(b) −1
(c) 0
(d) None of these.