# The Motion

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### Terminology

#### Kinematics:

• The branch of physics (mechanics) which deals with the motion of the bodies without considering the forces causing it is called kinematics.

#### Dynamics:

• The branch of physics (mechanics) which deals with the motion of the bodies and the forces causing it is called dynamics.

#### Body at Rest:

• A body is said to be at rest if it does not change its position with respect to its immediate surroundings.

#### Body in Motion:

• A body is said to be in motion if it changes its position with respect to its immediate surroundings.
• Note: Motion of a body is a relative concept.

#### One Dimensional Motion:

• When a body moves along a straight line path, is motion is called the one-dimensional motion or motion in a straight line or rectilinear motion.
• Example: the motion of a car along a straight road.
• For a moving body, if the distance travelled in a certain time interval is much larger as compared to the size of the body then body may be considered as a point body or point particle.

#### The Position of a Body or Particle:

•  Assuming the direction of the motion along the x-axis, the path of one-dimensional motion can be represented by a straight line parallel to x-axis then each point on the straight line represents the position of the particle at different instant of time. The position of the particle at any instant can be specified by its x-coordinate. The x-coordinate changes with time. #### Distance:

• The length of the path travelled by a body is called the distance travelled by it.
• Path of a body may not be straight.
• It is denoted by ‘s’ or ‘x’. Its S.I. unit is metre (m) and c.g.s. unit is centimetre (cm). Its dimensions are [L1M0T0]

#### Characteristics of Distance:

• It is the length of the path followed by the object in certain time. The path followed may or may not be along a straight line.
• It is a scalar quantity.
• It depends on the path followed by the object.
• It is always positive.
• It can be more than or equal to displacement.
• It may not be zero even if the displacement is zero.

#### Displacement:

• The shortest distance from the initial position to the final position of the body is called the magnitude of the displacement.
• It is vector quantity whose direction is from initial position to final position.
• Its S.I. unit is metre (m) and c.g.s. unit is centimetre (cm). Its dimensions are [L1M0T0]

#### Characteristics of Displacement:

• It is the shortest distance between the initial position to the final position of the body. It is always along a straight line.
• It is a vector quantity whose direction is from initial position to final position.
• It is independent of the path followed by the object.
• It may be positive, negative or zero.
• It may be equal but cannot be more than the distance travelled.
• It is zero when the distance travelled is zero. #### Notes:

Case – 1: When Distance travelled and displacement are equal.

• If an object moves along the positive direction of x-axis through 4m and further moves by 3 m in the same direction. In this case, the distance travelled by the object is 7m and displacement is also 7 m. Case – 2: When Distance travelled and displacement are not equal and displacement is positive

• If an object moves along the positive direction of x-axis through 4m and further moves by 3 m in the opposite direction. In this case, the distance travelled by the object is 7m and displacement is also + 1 m (along the positive direction of the x-axis). Case – 3: When Distance travelled and displacement are not equal and displacement is negative

• If an object moves along the positive direction of x-axis through 3m and further moves by 4 m in the opposite direction. In this case, the distance travelled by the object is 7m and displacement is also – 1 m (along the negative direction of the x-axis). Case – 4: When Distance travelled and displacement are not equal and displacement is zero

• If an object moves along the positive direction of x-axis through 4m and further moves by 4 m in the opposite direction. In this case, the distance travelled by the object is 8 m and displacement is also 0 m. #### Speed:

• The rate of change of distance with time is called the speed of the body.

Mathematically, speed = Distance/Time

• It is denoted by v. Its S.I. unit is m/s and c.g.s. unit is cm/s. Its dimensions are [L1M0T-1].
• Uniform Speed:
• A body is said to move with uniform speed if it covers equal distances in equal intervals of time throughout its motion.
• Non-Uniform or Variable Speed:
• A body is said to move at a non-uniform speed if it covers unequal distances in the same intervals of time.
• Instantaneous Speed:
• When a speed of a body changes continuously with time, its speed at any instant is known as instantaneous speed.
• Average Speed:
• The ratio of the total distance travelled by the body to the total time of journey is called average speed.
• When a body is moving with uniform speed, then the instantaneous speed and average speed are equal. #### Characteristics of Speed:

• The rate of change of distance with time is called the speed of the body.
• It is a scalar quantity
• Speed is always positive.
• In a circular motion, after executing complete circle, the average velocity of the body is zero but its average speed is not zero.

#### Velocity:

• The rate of change of displacement of a body with respect to time is called as the velocity of the body. • Velocity is a vector quantity, its S.I. unit is m/s and c.g.s. unit is cm/s.Its dimensions are [L1M0T-1]
• Uniform Velocity:
• When the magnitude and direction of the velocity of a body remain the same at any instant, then the body is said to have uniform velocity. For uniform motion acceleration a = 0 and Displacement = velocity × time.
• Example: The velocity of light in particular medium is uniform velocity.  The velocity of sound in air at constant temperature is uniform velocity.
• Non Uniform Velocity:
• When the magnitude of velocity or the direction of velocity or both changes at any instant the body is said to have nonuniform velocity or variable velocity.
• A body can have non-uniform velocity in following three cases.
• When the direction of the velocity of a body remains the same but its magnitude changes continuously then the body has variable velocity. e.g. a ball is thrown vertically upward.
• When the magnitude of the velocity of a body remains the same but the direction changes continuously then the body has variable velocity. e.g. uniform circular motion of a body.
• When both the magnitude and direction of the velocity of body change continuously, then the body has variable velocity. e.g. ball thrown by making the acute angle with the horizontal (projectile motion)
• When a body has variable velocity, then it has acceleration.
• Instantaneous Velocity:
• For body moving with non-uniform velocity, the velocity of the body at an instant is called instantaneous velocity.
• Average Velocity:
• If the velocity of a body moving in particular direction changes with time, then the ratio of displacement to total time is called average velocity.

#### Characteristics of Velocity:

• The rate of change of displacement of a body with respect to time is called as the velocity of the body.
• It is a vector quantity.
• The velocity can be positive, negative or zero.
• In a circular motion, after executing complete circle, the average velocity of the body is zero but its average speed is not zero.

#### Acceleration:

• The rate of change of velocity with respect to time is called acceleration. • Acceleration is vector quantity its S.I. unit is m/s2. Its dimensions are [L1M0T-2].
• Acceleration can be positive, negative or zero. If the velocity is increasing then acceleration is positive. If the velocity is decreasing acceleration is negative. If the velocity is constant acceleration is zero. Negative acceleration is also called deceleration or retardation.
• If the velocity is increasing then the direction of acceleration is same as that of the velocity of the body. If the velocity is decreasing then the direction of acceleration is opposite to that of the velocity of the body.
• It is to be noted that the velocity and not the acceleration of the body determines the direction of motion.
• Uniform Acceleration:
• When equal changes take place in velocity of a body in equal interval of time, then the acceleration is called uniform acceleration. e.g. the motion under gravity.
• Variable Acceleration:
• When The change in the velocity of a body in equal interval of time is not constant, then the acceleration is called non-uniform acceleration.

#### Acceleration Due To Gravity:

•  When the body falls freely under gravity, the acceleration produced in the body due to the gravitational force of attraction of the earth, then the acceleration by which the body falls down is called the acceleration of gravity.
• It is denoted by ‘g’. Its value is g = 9.8 m/s2. When solving problems on the motion under gravity as per the convention the value of ‘g’ should be negative.
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