#### Kerala PSC General Science Book Study Materials Page 5

Book's First PageEQUATIONS OF MOTION The equations of motion are used to Motion in Two Dimension describe various components of a moving object. The motion of an object is called two Displacement, velocity, time and dimensional, if two of the three co- ordinates are required to specify the acceleration are the kinematic variables position of the object in space changes that can be derived from these equations. w.r.t time. There are three equations, which are also In such a motion, the object moves in a referred to as the laws of constant plane. For example, a billiard ball moving acceleration, and therefore can only be over the billiard table, an insect crawling applied when acceleration is constant and over the floor of a room, earth revolving motion is constrained to a straight line. around the sun etc. The three equations are Two special cases of motion in two dimension are Projectile motion and Circular motion. v = u + at v2 = u2 + 2as Projectile Motion s = ut + 1⁄2at2 Projectile motion is a form of motion in Where which an object or particle (called a u = initial velocity (m/s) projectile) is thrown near the earth"s v = final velocity (m/s) surface, and it moves along a curved path a = acceleration (m/s2) under the action of gravity only. The only t = time (s) force of significance that acts on the object s = displacement (m) is gravity, which acts downward to cause a downward acceleration. Equation of motion under gravity Downward direction: Velocity of the projectile changes by v = u + gt acceleration vector in unit time. v2 = u2 + 2gs h = ut + 1⁄2gt2 The motion of a projectile is a two- Where g (gravitational acceleration) = 9.8 m/s2 dimensional motion. So, it can be Upward direction: discussed in two parts, Horizontal motion and vertical motion. These two motions take place independent of each other. v = u - gt The velocity of the particle can be v2 = u2 - 2gs resolved into two mutually perpendicular h = ut - 1⁄2gt2 components. Horizontal component and vertical component. Where g (gravitational acceleration) = -9.8 The horizontal component remains m/s2 unchanged throughout the flight. The force of gravity continuously affects the vertical component. Distance travelled by a body in nth second The horizontal motion is a uniform motion Snth = u + (2n-1) a/2 and the vertical motion is a uniformly accelerated retarded motion. h = height, nth = time interval 4

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