Question

1. Derive motions formulas:
a) By Graphical method
b) By General method ​

Answer 1

Answer:

I'll do b) only as I can't do a) right now sorry

The general method is using calculus, as I've done below

Step-by-step explanation:

i) a=dv/dt

adt=dv

Integrating on both sides

a∫dt=∫dv

a t (limits 0 to t)=v (Limits u to v)              (a is constant)

at=v-u

v-u=at

v=u+at

ii) v=dx/dt

vdt=dx

Use v=u+at from above

(u+at)dt = dx

udt + atdt = dx

Integrating on both sides

u∫dt + a∫tdt = ∫dx

u t (Limits 0 to t) + a (t^2/2)(Limit 0 to t) = x(Limit 0 to s)

ut + (at^2)/2 = s

s= ut + 1/2 at^2

iii)v=dx/dt

Multiplying up and down by dv

v = dx/dt * dv/dv

We know dv/dt=a

v=adx/dv

vdv = adx

Integrating on both sides

∫vdv = a∫dx

v^2/2 (Limit u to v) = a x(Limit 0 to s)

(v^2-u^2)/2 = as

v^2-u^2 = 2as

Voila! There you go

All the equations have been derived

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Thank You!!