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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.
Distance and Displacement
- Distance: The total length of path covered by an object is said to be the distance travelled by it.
- Displacement: The length of a straight path that joins the initial and final positions of an object is known as the displacement.
Difference Between Displacement and Displacement
|Distance is defined as the total length of the path traveled by an object to go from one point to another.||Displacement is defined as the length of the straight path 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: 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: 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
|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: Change in the velocity of an object per unit time.
Derivation Of Equations Of Motion
Derivation of The Equations of Motion By Algebraic Method:
Derivation of S = ut + ½ at2
Derivation of v2 – u2 = 2as
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
(a) Velocity-time relation:
(ii) The equation for position-time relation:
(iii) Equation for position-velocity relation:
Conclusions From a Distance – Time Graph