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.