Rest And Motion

• Motion: An object is said to be in motion when its position changes 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.
• A specific point with respect to which we describe the location of an object is called a reference point.
• The terms Rest and Motion are relative. (Scroll down to continue …)

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

Distance	Displacement
Distance is defined as the total length of the path travelled by an object to go from one point to another.	Displacement is defined as the  length of the line segment that joins the initial and final positions of an object.
Since distance has only magnitude and its direction cannot be specified always, it  is a scalar quantity.	Since displacement has magnitude and it  is specified in a direction  from initial position to final position, it is a vector quantity.
Distance can only have positive values.	Displacement can have both positive and negative values.
Distance depends on the length of the path travelled.	Displacement depends only on the initial and final point regardless of the path travelled.

Speed And Velocity Speed

• 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.
• Average speed: For non-uniform motion, the average speed of an object is obtained by dividing the total distance travelled by an object by the total time taken.

• For a uniform motion, the average speed of an object is equal to its instantaneous speed throughout the path.

Velocity

• Average Velocity or Velocity : For a uniform motion in a straight path, the average velocity is equal to its instantaneous velocity throughout the path.

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

Differences Between Speed and Velocity

SPEED	VELOCITY
It is defined as the rate of change of distance.	It is defined as the rate of change of net displacement.
It is a scalar quantity.	It is a vector quantity.
It can never be negative or zero.	It can be negative,zero or positive.
Speed is velocity without direction.	Velocity is directed speed.
Speed may or may not be equal to velocity.	A body may possess different velocities but the same speed.
Speed never decreases with time. For a moving body,	Velocity can decrease with time. For a moving body , it can be zero.
Speed is never zero.	Velocity can be zero.
Speed in SI is measured in ms-1	Velocity in SI, is measured in ms-1

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.