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- 1. Rectilinear Motion
- 2. Important Terms And Definitions 1. Kinematics : It is the branch of dynamics which deals with the forces acting on bodies in motion without considering the mass of a body and the forces which is responsible to cause the motion.
- 3. Rectilinear Motion Motion of a particle along a straight line is called rectilinear motion, linear motion or one dimensional motion.
- 4. 3. To describe linear motion of a particle its position at all times is to be specified. The equations used in this case are called ‘Equations of Motion’ or ‘Kinematical equations’.
- 5. 4. Every motion is related to the observer: Position of a particle in motion is described in terms of distance from reference point or origin.
- 6. Path length or distance travelled : The total distance covered by a particle during its motion is called path length or distance traveled (scalar quantity)
- 7. Displacement : Change in position of a moving particle in a particular direction is called displacement. Displacement is the shortest distance between two positions of a moving particle in a particular direction (vector quantity)
- 8. Displacement and distance traveled are equal in rectilinear motion but distance traveled is greater than displacement in any other motion.
- 9. Average velocity (vector quantity) The average velocity of a moving particle is defined as the displacement divided by the interval in which it has occurred avg vel V x t
- 10. Average speed : Average speed of a moving particle is defined as total distance travelled divided by time taken Avg speed V = total distance traveled / time
- 11. Acceleration : Acceleration of a moving body is defined as the rate of change of velocity with respect to time.
- 12. Equation of motion, when Distance (s) Travelled by a Body Moving with a Uniform Velocity: We know that, Distance travelled = Average velocity x time S u v t 2 we have, v = u + at, substitute this in equation (1), we get
- 13. Equation of Motion, when Velocity of a Body Moving with Uniform Acceleration after Covering a Distance ‘S’
- 14. Equation of Motion, when a Distance Travelled in nth Second by a particle (or Body) Moving with Uniform Acceleration: Consider a body in rectilinear motion moving with initial velocity (u) and uniform acceleration (a). In nth second, it acquires a velocity (v) and covers a distance (s). u = Initial velocity of a body: v = Final velocity of a body n = Number of second: sn = Distance travelled in n sec.
- 15. Distance covered in (n – 1) sec. Distance travelled in nth sec. = sn – sn-1 A = Uniform acceleration. From Equation (2), we have sn-1 = snth = For distance travelled in n second, put t = n
- 16. For distance travelled in (n – 1) second, put t = n – 1
- 17. Graphical Representation Velocity Time Graph Case I Uniform velocity Area under the curve = displacement S = Vt
- 18. Case II:- When the body moves with a variable velocity: = s = distance travelled. If velocity varies from 0 to v, V-T diagram is a triangle as shown in fig. Here initial velocity (u) is zero. Area under the graph = Area of a triangle
- 19. s = distance travelled.
- 20. If velocity varies from u to 0. (Final velocity (v) is zero): V-T diagram is a triangle as shown in Area under the graph = Area of a rectangle 1 2 1 2 1 2 1 2 OB u t v at t .... s in c e u = v - a t 0 at t ....s in c e v = 0 1 2 s OA at 2 d is ta n c e tra v e lle d
- 21. Negative sign indicates that there is retardation. S lo p e u t ta n a u t .....sin ce -a = re ta rd a tio n .
- 22. If velocity varies from u to v: VT diagram is trapezium as shown in fig. Area under the graph = Area of trapezium

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