Question

derive the three equation of motion graphically :-
1) v= u + at
2) S = ut + 1/2 at^2
3) v^2 = u^2 + 2aS

give suitable diagram.

Answer 1

I can derive only 1st equation by graphically but mathematically I can derive all three equation.

Answer 2

Answer:

Equation of Motion (For Uniformly Accelerated Motion)

(1) First Equation

v = u + at

Or, Final velocity = Initial velocity + Acceleration × Time

Graphical Derivation :

Suppose a body has Initial velocity 'u' (i.e., velocity at t = 0 sec.) at point 'A' and this velocity changes to 'v' at point 'B' in 't' secs. i.e., Final velocity will be 'v'.

For Such a body there will be an Acceleration.

a = Change in Velocity / Change in time

a = (OB-OA)/(OC-0) = (v-u)/(t-0)

a = (v-u)/t

Or

Or v = u + at

(2) Second Equation

s = ut + 1/2at ^2

Distance travelled by object = Area of OABC

= Area of OADC +

Area of ∆ ABD

= OA×A+1/2×AD×BD

= u × t + 1/2 × (v-u)

[:(v-u)/t =a] So {v-u=at) = ut + 1/2 × t× at

s = ut + 1/2at ^2

(3) Third Equation

v^2 = u^2 + 2aS

s = Area of trapezium OABC

s = [(OA + BC)×OC]/2

s = [(u + v)×t]/2

s = [(u+v)/2] × [(v-u)/a]

s = (v^2-u^2)/2a

Or, v^2 = u^2 + 2as