Rest And Motion

Motion: An object is said to be in motion when its position changes with respect to the reference point with time.

Rest: An object is said to be at rest when its position does not change with respect to a reference point with time.

Reference Point:

A specific point with respect to which we describe the location of an object is called a reference point.

A body can be at rest as well as in motion at the same time with respect to two different reference points.

Therefore, Rest and Motion are relative terms not absolute terms.

Rest and Motion are relative tems. Since a body may be at rest relative to one object and simultaneously it may be in motion relative to another object.

Example: a passenger sitting in a moving vehicle is at rest with respect to his fellow passenger but he is in motion with respect to a place outside the bus.

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Distance and Displacement

• Distance: The total length of path covered by an object is said to be the distance travelled by it.
• Displacement: Gap between the initial and final positions of an object is said to be its displacement. Or
• The length of a line segment that joins the initial and final positions of an object is known as the displacement.

Difference Between Displacement and Displacement

Speed And Velocity

Speed:

• Speed or Average Speed: The distance travelled by an object in unit time is referred to as speed. 
• Its S.I unit is m/s. 
• In general speed refers to average speed.
• For non-uniform motion, the average speed of an object is obtained by dividing the total distance travelled by an object with the total time taken.

• Instantaneous Speed:
• Speed of a body at an instant, that is at a very short span is known as Instantaneous Speed.
• For a uniform motion, the average speed of an object is equal to its instantaneous speed throughout the path.

Velocity

Velocity Or Average Velocity:

• In case of a uniform motion in a straight path, the average velocity is equal to its instantaneous velocity throughout its path.

• Velocity (average velocity) of an object is equal to the instantaneous velocity of an object.

Differences Between Speed And Velocity

Uniform And Non-Uniform motion

• Uniform motion or non accelerated motion: When an object covers equal distances in equal intervals of time, it is said to be in uniform motion. Uniform motion is a non-accelerated motion.
• Non-uniform motion or accelerated motion: Motions where objects cover unequal distances in equal intervals of time. Uniform motion is an accelerated motion.

Acceleration

Acceleration: Change in the velocity of an object per unit time.

Graphical representation of motions

(i) Distance-time graph

For a distance-time graph, time is taken on x-axis and distance is taken on the y-axis.

[Note: All independent quantities are taken along the x-axis and dependent quantities are taken along the y-axis.]

(ii) Velocity-time graph

Equation of motion by graphical methods

Derivation Of Equations Of Motion

Equations of motion can be derived by two methods. They are (i) Graphical Method. (ii) Algebraic Method

Derivation of The Equations of Motion By Algebraic Method:

(a) Velocity-time relation:

Derivation of S = ut + ½ at²

(ii) The equation for position-time relation:

Derivation of v² – u²  = 2as

(iii) Equation for position-velocity relation:

Conclusions From a Distance – Time Graph

Uniform Circular Motion

When a body moves in a circular path with uniform speed, its motion is called uniform circular motion.