Kinematic Equations for Uniformly Accelerated Motion
1. Graphical Method
a). For First Law of
Motion
If a object moving with constant acceleration so the change
in velocity is constant. So in this velocity time graph is a straight line as
shown in figure.
So dv / dt = a = tan θ
tan θ = AC / BC = a = constant
a = ( v – u ) / t
a t = v – u
v = u + a t …..(1)
It is the first law of motion.
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| science-class-9 |
Distance ( s ) = Area of ACDOB
= ½ * (Sum of parallel sides) * Altitude
= ½ * ( OB + AD ) * BC
= ½ * ( u + v ) * t ….(2)
Putting the value of equation 1 in equation 2
S = ½ * ( u + u + a t ) * t
= ½ * ( 2u + a t )
* t
S = u t + ½ * a * (t ^ 2)
It is the second law of motion.
c). For Third Law of Motion
S = ½ *
( u + v ) * t ….(3)
By equation 1
V = u + a t
V – u = a t
t = ( v – u ) / t ….(4)
Putting this value in equation (3)
S = ½ *
( u + v ) * t
= ½ * {( v –
u ) ( v + u ) / a )
2 a s = ( v + u ) ( v – u )
2 a s = v^2 – u^2
v^2 = u^2 + 2 a s
It is the third law of motion.
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