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**Facts that Matter **

- An object is said to be in motion when its position changes with time.
- We describe the location of an object by specifying a reference point. Motion is relative. The total path covered by an object is said to be the distance travelled by it.
- The shortest path/distance measured from the initial to the final position of an object is known as the displacement.
**Uniform motion:**When an object covers equal distances in equal intervals of time, it is said to be in uniform motion.**Non-uniform motion:**Motions where objects cover unequal distances in equal intervals of time.**Speed:**The distance travelled by an object in unit time is referred to as speed. Its unit is m/s.**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.

**Velocity**: Velocity is the speed of an object moving in definite direction. S.I. unit is m/s.

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

**(ii) Velocity-time graph**

**Equations of motion by graphical method**

(i) Velocity-time relation: v

**(ii) Equation for position-time relation:**

Let us assume,

s = distance travelled by the object

t = time t

a = uniform acceleration.

∴ Distance travelled by the object is given by area enclosed with OABC in the graph.

∴ s = area OABC (which is a trapezium)

= (area of rectangle OADC) + (area of ∆ABD)

Substituting OA = u, OC = AD = t and BD = at (from equation 2)

**(iii) Equation for position–velocity relation:**

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

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