Motion-Speed, Velocity , Acceleration

<–2/”>a >Motion

Motion is a change in position of an object with respect to time. Motion is typically described in terms of displacement, distance, velocity, acceleration, time and speed.

The branch of physics which deals with the study of motion of material objects is called mechanics.

Mechanics is divided into following branches.

(i) Statics : Statics is the branch of mechanics which deals with the study of motion of objects under the effect of forces in equilibrium.

(ii) Kinematics :

It is that branch of mechanics which deals with the study of motion of object without taking into account the factors (i.e. nature of forces, nature of bodies etc.) which cause motion. Here time factor plays an essential role.

(iii) Dynamics :

It is that branch of mechanics which deals with the study of motion of objects taking into account the factors whichcause motion.

Rest : An object is said to be at rest if it does not change its position with time, with respect to its surroudings.

A book lying on a table, a person sitting in a chair are the examples of rest.

Motion : An object is said to be in motion if it changes its position with time, with respect to its surroundings.

Example : A bird flying in air, a train moving on rails, a ship sailing on water, a man walking on road are some of the examples of motion, visible to the eye. Motion of gas Molecules is an example of motion, invisible to the eye.

Rest & Motion are relative terms :

When we say that an object is at rest or in motion,then this statement is incomplete and meaningless. Basically, rest & motion are relative terms. An object which is at rest can also be in motion simultaneously. This can be illustrated as follows.

The passengers sitting in a moving bus are at rest with respect to each other but they are also in motion at the same time with respect to the objects like trees, buildings on the road side. So the motion and rest are relative terms.

Rectilinear motion :

If a particle moves in a fixed direction, the motion of this type is called rectilinear motion or one dimensional motion.For example the motion of an ant on a wire is a rectilinear motion.

Two dimensional motion :

If the motion of a particle is in such a way that its position remains on a fixed plane, then the motion of a particle is called two dimensional motion.

Laws Of Motion

First Law of Motion

A body continue to be in its state of rest or of uniform motion along a straight line, unless it is acted upon by some external force to change the state

(1) If no net force acts on a body, then the velocity of the body cannot change i.e. the body cannot accelerate.

(2) Newton‟s first law defines inertia and is rightly called the law of inertia. Inertia are of three types :Inertia of rest, Inertia of motion, Inertia of direction

(3) Inertia of rest : It is the inability of a body to change by itself, its state of rest. This means a body atrest remains at rest and cannot start moving by its own.

Second Law of Motion

(1) The rate of change of linear momentum of a body is directly proportional to the external force appliedon the body and this change takes place always in the direction of the applied force.

(2) If a body of mass m, moves with velocity v then its linear momentum can be given by p= mv and if force is applied on a body, then Force = mass ? acceleration

Third Law of Motion

To every action, there is always an equal (in magnitude) and opposite (in direction) reaction.

(1) When a body exerts a force on any other body, the second body also exerts an equal and opposite forceon the first.

(2) Forces in nature always occurs in pairs. A single isolated force is not possible.

(3) Any agent, applying a force also experiences a force of equal magnitude but in opposite direction. Theforce applied by the agent is called „Action‟ and the counter force experienced by it is called „Reaction‟.

(4) Action and reaction never act on the same body. If it were so the total force on a body would have always been zero i.e. the body will always remain in equilibrium.

(5) If F (AB)= force exerted on body A by body B (Action) and F(BA)= force exerted on body B by body A (Reaction) Then according to Newton‟s third law of motion F (AB) = F(BA)

(6) Example : (i) A book lying on a table exerts a force on the table which is equal to the weight of the book. This is the force of action.

Linear motion

Linear motion, also called uniform motion or rectilinear motion, motion in one spatial dimension.  According to Newton’s first law (also known as the principle of inertia), a body with no net force acting on it will either remain at rest or continue to move with uniform speed in a straight line, according to its initial condition of motion. In fact, in classical Newtonian mechanics, there is no important distinction between rest and uniform motion in a straight line; they may be regarded as the same state of motion seen by different observers, one moving at the same velocity as the particle, the other moving at constant velocity with respect to the particle.  A body in motion may be said to have momentum equal to the product of its mass and its velocity. It also has a kind of energy that is entirely due to its motion, called kinetic energy. The kinetic energy of a body of mass m in motion with velocity v is given by K = (1/2)mv2.

Speed and Velocity

Both speed and velocity tell us how far something is travelling in unit time. As velocity is a vector it must also tell us what direction the object is travelling in.

Average velocity v̅ = Δs / Δt

Acceleration

Acceleration tells us how rapidly something is changing velocity – for instance, the change in velocity in unit time.Deceleration is the same thing, but has a negative sign as the velocity if decreasing.

Velocity-time graphs

These are similar to displacement-time graphs, but this time velocity is on the y-axis. Here are the only possibilities that you’ll come across at A-level.

gradient = change in V  (or ΔV) / change in t (or Δt) = the acceleration at any time.

Circular motion

When an object moves in a circle at a constant speed its velocity (which is a vector) is constantly changing. Its velocity is changing not because the magnitude of the velocity is changing but because its direction is. This constantly changing velocity means that the object is accelerating (centripetal acceleration).  For this acceleration to happen there must be a resultant force, this force is called the centripetal force.

Angular Speed

The angular speed (w) of an object is the angle (q) it moves through measured in radians (rad) divided by the time (t) taken to move through that angle. This means that the  unit for angular speed is the radian per second (rad s-1).

v is the linear velocity measured in metres per second (ms^-1).

r is the radius of the circle in metres (m).

f is the frequency of the rotation in hertz (Hz).

Centripetal Acceleration

Centripetal acceleration (a) is measure in metres per second per second (ms-2). It is always directed towards the center of the circle.

Centripetal Force

When an object moves in a circle the centripetal force (F) always acts towards the centre of the circle. The centripetal force, measured in newtons (N) can be different forces in different settings it can be gravity, friction, tension, lift, electrostatic attraction etc.

Vibrationational motion

periodic back-and-forth motion of the particles of an elastic body or medium, commonly resulting when almost any physical system is displaced from its equilibrium condition and allowed to respond to the forces that tend to restore equilibrium.

Vibrations fall into two categories: free and forced. Free vibrations occur when the system is disturbed momentarily and then allowed to move without restraint. A classic example is provided by a weight suspended from a spring. In equilibrium, the system has minimum energy and the weight is at rest. If the weight is pulled down and released, the system will respond by vibrating vertically.

The vibrations of a spring are of a particularly simple kind known as simple harmonic motion (SHM). This occurs whenever the disturbance to the system is countered by a restoring force that is exactly proportional to the degree of disturbance. In this case, the restoring force is the tension or compression in the spring, which (according to Hooke’s law) is proportional to the displacement of the spring. In simple harmonic motion, the periodic oscillations are of the mathematical form called sinusoidal.

Most systems that suffer small disturbances counter them by exerting some form of restoring force. It is frequently a good approximation to suppose that the force is proportional to the disturbance, so that SHM is, in the limiting case of small disturbances, a generic feature of vibrating systems. One characteristic of SHM is that the period of the vibration is independent of its amplitude. Such systems therefore are used in regulating clocks. The oscillation of a pendulum, for instance, approximates SHM if the amplitude is small.

A universal feature of free vibration is damping. All systems are subject to frictional forces, and these steadily sap the energy of the vibrations, causing the amplitude to diminish, usually exponentially. The motion is therefore never precisely sinusoidal. Thus, a swinging pendulum, left undriven, will eventually return to rest at the equilibrium (minimum-energy) position.

Forced vibrations occur if a system is continuously driven by an external agency. A simple example is a child’s swing that is pushed on each downswing. Of special interest are systems undergoing SHM and driven by sinusoidal forcing. This leads to the important phenomenon of resonance. Resonance occurs when the driving frequency approaches the natural frequency of free vibrations. The result is a rapid take-up of energy by the vibrating system, with an attendant Growth of the vibration amplitude. Ultimately, the growth in amplitude is limited by the presence of damping, but the response can, in practice, be very great. It is said that soldiers marching across a bridge can set up resonant vibrations sufficient to destroy the structure. Similar folklore exists about opera singers shattering wine glasses.

Electric vibrations play an important role in electronics. A circuit containing both inductance and capacitance can support the electrical equivalent of SHM involving sinusoidal current flow. Resonance occurs if the circuit is driven by alternating current that is matched in frequency to that of the free oscillations of the circuit. This is the principle behind tuning. For example, a radio receiver contains a circuit, the natural frequency of which can be varied. When the frequency matches that of the radio transmitter, resonance occurs and a large alternating current of that frequency develops in the circuit. In this way, resonating circuits can be used to filter out one frequency from a mixture.

In Musical instruments, the motion of strings, membranes, and air columns consists of a superposition of SHM’s; in engineering structures, vibrations are a common, though usually undesirable, feature. In many cases, complicated periodic motions can be understood as the superposition of SHM at many different frequencies.

SPEED

An object is said to be in motion if it changes its position with time, with respect to its surroundings.Speed is defined as the distance moved per unit time,

i.e Speed =Distance /Time

When we say that an object is at rest or in motion,then this statement is incomplete and meaningless. Basically, rest & motion are relative terms.
An object which is at rest can also be in motion simultaneously. This can be illustrated as follows.
The passengers sitting in a moving bus are at rest with respect to each other but they are also in motion at the same time with respect to the objects like trees, buildings on the road side. So the motion and rest are relative terms.

VELOCITY

Velocity indicates the rate of change of the object’s position (r  ); i.e., velocity tells you how fast the object’s position is changing. The magnitude of the velocity (|| v ||  ) indicates the object’s speed. The direction of the velocity (dir v  ) indicates the object’s direction of motion. The velocity at any point is always tangent to the object’s path at that point. Thus, the velocity tells you how the object is moving. In particular, the velocity tells you which way and how fast the object is moving.

MASS

It is the measure of the quantity of matter in an object and its unit is kilogram (kg) in SI units. It depends on the number of molecules in the matter and their masses and does not depend on gravity. Therefore an object would have same mass on Earth and on the Moon but different weight because of the change of gravity. Gravity on the moon is 1/6th of the gravity on earth. Mass of an object can be measured by using spring balance (newton-meter), top pan balance or lever balance. The international definition of mass is It is equal to the mass of the international prototype of the kilogram made up of platinum-iridium Alloy kept at international bureau of weights and measurements in Paris.

Mass is the amount of matter in an object. It can also be defined as the property of a body that causes it to have weight in a gravitational field. It is important to understand that the mass of an object is not dependent on gravity. Bodies with greater mass are accelerated less by the same force.

WEIGHT

The weight of an object is defined as the force of gravity on the object and may be calculated as the mass times the acceleration of gravity, w = mg. Since the weight is a force, its SI unit is the newton.

For an object in free fall, so that gravity is the only force acting on it, then the expression for weight follows from Newton’s second law.

FORCE

Force is any interaction that, when unopposed, will change the motion of an object. A force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate.

IMPACT

Impact is a high force or shock applied over a short time period when two or more bodies collide. Such a force or acceleration usually has a greater effect than a lower force applied over a proportionally longer period.

WORK

Work is said to be done when a force applied on the body displaces the body through a certain distance in the direction of force.Mathematically, work is the force-displacement product

W = F x s cos a

or the force-displacement path integral

dW = F · ds

Positive work means that force (or its component) is parallel to displacement. Negative work means that force (or its component)is opposite to displacement i.e. In conservative field work done by the force over a closed loop is zero.

POWER

Power is defined as the rate at which work is done. Its unit is watt Power is said to be one watt, when one joule of work is said to be done in one second.

If work is being done by a machine moving at speed v against a constant force, or resistance, F, then since work done is force times distance, work done per second is Fv, which is the same as power.
Power = Fv

ENERGY

Energy is the capacity for doing work. Energy can manifest itself in many forms like mechanical energy, thermal energy, electric energy, chemical
energy, Light energy, Nuclear Energy, etc.
The energy possessed by a body due to its position or due to its motion is called mechanical energy. The mechanical energy of a body consists of potential energy and kinetic energy.
Potential energy is the energy of a body or a system with respect to the position of the body or the arrangement of the particles of the system.For example, gravitational potential energy is associated with the Gravitational Force acting on object’s mass; elastic potential energy with the elastic force (ultimately electromagnetic force) acting on the elasticity of a deformed object; electrical potential energy with the coulombic force; strong nuclear force or weak nuclear force acting on the electric charge on the object; chemical potential energy, with the chemical potential of a particular atomic or molecular configuration acting on the atomic/molecular structure of the chemical substance that constitutes the object; thermal potential energy with the electromagnetic force in Conjunction with the temperature of the object.

Kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.

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Motion is the change of position of an object over time. Motion can be described in terms of speed, velocity, and acceleration.

Speed is the rate at which an object moves. It is measured in units of distance per unit time, such as meters per second (m/s) or kilometers per hour (km/h). Speed can be constant, or it can change. If speed is constant, the object is said to be moving at a uniform speed. If speed is changing, the object is said to be accelerating.

Velocity is the rate at which an object changes its position. It is a vector quantity, which means that it has both magnitude and direction. Velocity is measured in units of distance per unit time, such as meters per second (m/s) or kilometers per hour (km/h). The direction of velocity is the same as the direction of the object’s motion.

Acceleration is the rate at which an object’s velocity changes. It is also a vector quantity, which means that it has both magnitude and direction. Acceleration is measured in units of meters per second squared (m/s^2). The direction of acceleration is the same as the direction of the object’s change in velocity.

Average speed is the total distance traveled divided by the total time taken. It is a scalar quantity, which means that it has only magnitude. Average speed can be calculated for any type of motion, whether it is constant or variable.

Instantaneous speed is the speed of an object at a particular instant in time. It is calculated by taking the limit of the average speed as the time interval approaches zero. Instantaneous speed is a vector quantity, which means that it has both magnitude and direction.

Average velocity is the total displacement divided by the total time taken. It is a vector quantity, which means that it has both magnitude and direction. Average velocity can be calculated for any type of motion, whether it is constant or variable.

Instantaneous velocity is the velocity of an object at a particular instant in time. It is calculated by taking the limit of the average velocity as the time interval approaches zero. Instantaneous velocity is a vector quantity, which means that it has both magnitude and direction.

Average acceleration is the change in velocity divided by the time taken for the change to occur. It is a vector quantity, which means that it has both magnitude and direction. Average acceleration can be calculated for any type of motion, whether it is constant or variable.

Instantaneous acceleration is the acceleration of an object at a particular instant in time. It is calculated by taking the limit of the average acceleration as the time interval approaches zero. Instantaneous acceleration is a vector quantity, which means that it has both magnitude and direction.

The following are some examples of motion:

• A car moving down the road.
• A ball rolling down a hill.
• A bird flying through the air.
• A rocket launching into space.

In each of these examples, the object is moving from one position to another. The rate at which the object moves is its speed. The direction in which the object moves is its velocity. The rate at which the object’s velocity changes is its acceleration.

Motion is a fundamental concept in physics. It is used to describe the movement of objects in space and time. Motion can be studied in terms of its speed, velocity, and acceleration.

1. What is force?

Force is an interaction between two objects that causes a change in motion.

2. What is mass?

Mass is a measure of how much matter is in an object.

3. What is weight?

Weight is the force of gravity on an object.

4. What is inertia?

Inertia is the tendency of an object to resist a change in motion.

5. What is momentum?

Momentum is the product of mass and velocity.

6. What is energy?

Energy is the ability to do work.

7. What is work?

Work is the transfer of energy from one object to another by means of a force.

8. What is power?

Power is the rate at which work is done.

9. What is torque?

Torque is the rotational equivalent of force.

10. What is angular momentum?

Angular momentum is the rotational equivalent of momentum.

11. What is a lever?

A lever is a simple machine that consists of a beam or rod that pivots on a fulcrum.

12. What is a pulley?

A pulley is a simple machine that consists of a grooved wheel with a rope or cable that runs around it.

13. What is a wedge?

A wedge is a simple machine that consists of a thin piece of Metal or wood that is used to split or separate objects.

14. What is a screw?

A screw is a simple machine that consists of a cylindrical rod with a helical groove that is used to fasten objects together.

15. What is a nail?

A nail is a thin piece of metal with a pointed end that is used to fasten objects together.

16. What is a bolt?

A bolt is a cylindrical rod with a head and a threaded end that is used to fasten objects together.

17. What is a nut?

A nut is a cylindrical piece of metal with a threaded hole that is used to fasten objects together with a bolt.

18. What is a gear?

A gear is a toothed wheel that is used to transmit power from one part of a machine to another.

19. What is a chain?

A chain is a series of links that are connected together and used to transmit power from one part of a machine to another.

20. What is a belt?

A belt is a flexible band that is used to transmit power from one part of a machine to another.

Sure, here are some MCQs without mentioning the topic Motion-Speed, Velocity , Acceleration:

1. A car is moving at a constant speed of 60 km/h. What is the car’s acceleration?
   (A) 0 m/s^2
   (B) 60 m/s^2
   (C) 100 m/s^2
   (D) 120 m/s^2

2. A ball is thrown straight up into the air. What is the ball’s acceleration at the top of its flight?
   (A) 9.8 m/s^2 downward
   (B) 0 m/s^2
   (C) 9.8 m/s^2 upward
   (D) 19.6 m/s^2 upward

3. A car accelerates from 0 to 60 km/h in 5 seconds. What is the car’s average acceleration?
   (A) 12 m/s^2
   (B) 36 m/s^2
   (C) 72 m/s^2
   (D) 108 m/s^2

4. A train is moving at a speed of 100 km/h. The train then accelerates at a rate of 2 m/s^2. What is the train’s speed after 5 seconds?
   (A) 102 km/h
   (B) 104 km/h
   (C) 106 km/h
   (D) 108 km/h

5. A ball is thrown straight up into the air. The ball reaches a height of 20 meters. What was the ball’s initial speed?
   (A) 14.7 m/s
   (B) 29.4 m/s
   (C) 44.1 m/s
   (D) 58.8 m/s

6. A car is moving at a speed of 60 km/h. The car then brakes and comes to a stop in 5 seconds. What is the car’s acceleration?
   (A) -12 m/s^2
   (B) -36 m/s^2
   (C) -72 m/s^2
   (D) -108 m/s^2

7. A ball is thrown straight up into the air. The ball takes 2 seconds to reach its maximum height. What was the ball’s initial speed?
   (A) 14.7 m/s
   (B) 29.4 m/s
   (C) 44.1 m/s
   (D) 58.8 m/s

8. A car is moving at a speed of 60 km/h. The car then accelerates to a speed of 120 km/h in 5 seconds. What is the car’s acceleration?
   (A) 36 m/s^2
   (B) 72 m/s^2
   (C) 108 m/s^2
   (D) 144 m/s^2

9. A ball is thrown straight up into the air. The ball reaches a height of 20 meters and then falls back down. What is the ball’s speed when it hits the ground?
   (A) 14.7 m/s
   (B) 29.4 m/s
   (C) 44.1 m/s
   (D) 58.8 m/s

10. A car is moving at a speed of 60 km/h. The car then brakes and comes to a stop in 2 seconds. What is the car’s acceleration?
    (A) -36 m/s^2
    (B) -72 m/s^2
    (C) -108 m/s^2
    (D) -144 m/s^2