```                                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
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