Title KINEMATICS.pdf ✅

CLASS VIII PHYSICS Introduction: The study of motion of bodies not considering the cause of motion is called Kinematics. Recap of previous class synopsis. Equations of Motion: When particle moves with zero acceleration: a) It is unidirectional motion with constant speed b) Magnitude of displacement is always equal to the distance travelled c) v = u, s = ut[ as a = 0] When particle moves with non zero acceleration: a) acceleration is said to be constant when both the magnitude and direction of acceleration remains constant. b) Equation of motion in scalar form v = u + at s = ut + 1 2 at2 v 2 − u 2 = 2as s = ( u + v 2 ) t sn = u + a 2 (2n − 1) Equation of motion in vector form v⃗ = u⃗ + a⃗⃗⃗t s = u⃗⃗⃗t + 1 2 a⃗ t 2 v⃗ 2 − u⃗ 2 = 2a⃗ s s = ( u⃗ + v⃗ 2 ) t s n = u⃗ + a⃗ 2 (2n − 1) Motion in One Dimension: In One-Dimension, the position of a particle is completely described by using one co-ordinate only. In 1D mo- tion initial velocity and acceleration are parallel or anti parallel to each other. MOTION UNDER GRAVITY: The uniform acceleration of a free falling body towards the centre of the earth due to earth's gravitational force is called acceleration due to gravity. It is denoted by ' g '. Its direction is always towards to the centre of the earth. The average value of g on the earth surface is 9.8 ms−2 or 980cms−2 and that of the moon is 1.63 ms−2 ( gearth /6). i) Free Fall Body: Motion of all bodies falling towards the earth when air resistance is ignored is known as free fall. For free fall, u = 0, a = +g and s = h a) v = gt c) v 2 = 2gh b) h = 1 2 gt 2 KINEMATICS SYNOPSIS - 1
CLASS VIII PHYSICS d) hn = 1 2 g(2n − 1) ii) Projected Vertically Upward: For a body projected vertically upwards, u ≠ 0, a = −g( since velocity and acceleration vectors are opposite) Maximum height : The vertical distance travelled by a body before its velocity becomes zero is called maxi- mum height reached by the body. we know that, v 2 − u 2 = 2a here, a = −g, s = h, V = 0 ⇒ 0 2 − u 2 = −2gh ⇒ u 2 = 2gh ⇒ h = u 2 2 g . Time of ascent : Time taken by the body to reach the highest point is called time of ascent (ta ). Here a = −g,t = ta , V = 0, v = u − gta; o = u − gta ⇒ ta = u g Time of descent : Time taken by the body to travel from the maximum height to the ground is called time of descent (td ). here, u = 0, a = +g,t = td, V = 0 + gtd ⇒ td = u g . In the absence of air resistance, time of as- cent is equal to time of descent. Time of flight: The total time spent by the body in air is called time of flight (t) is given by t = ta + td = u g + u g = 2u g Velocity on reaching the ground: When a body is dropped from a height h, its initial velocity is zero. Let the final velocity on reaching the ground be v. For a freely falling body, v 2 − u 2 = 2gh, but u = 0 therefore, v 2 − 0 2 = 2gh ⇒ v 2 = 2gh ⇒ v = √2gh Velocity of the body falling from height h, on reaching the ground is equal to the velocity with which it is pro- jected vertically upwards to reach the same height h. The upwards velocity at any point in its flight is the same as its downward velocity at that point. Body projected vertically up from the top of a tower: If a body is projected vertically up from the top of a tower of height ' h ' with velocity ' u '. a) Displacement after time t is S = ut − 1 2 gt2 b) If it reaches the ground after time t, then −h = ut − 1 2 gt2 c) Its velocity on reaching the ground is √u 2 + 2gh d) Its maximum height above the ground is {h + (u 2 /2 g)} APPLICATIONS: 1. Change in velocity in the entire journey is 2u(ΔV = v − u = u − (−u) = 2u) 2. Change in momentum during the entire journey is 2mu 3. Velocity at half of the maximum height is u √2 (Hint: v 2 − u 2 = −2gh ⇒ v 2 = −2 g Hmax 2 + u 2 ⇒ v 2 = u 2 2 ) 4. Distance covered projected vertically up in the last one second of its upwards journey equal to distance covered by it in the first second of free fall = g 2
CLASS VIII PHYSICS 5. When air resistance is taken into account, a) Time of ascent less than time of descent. b) Speed of the body when it reaches the point of projection is less than the speed of projection. DISPLACEMENT TIME GRAPHS: