EQUATIONS 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