Question

prove v^2=u^2+2as by calculus

Answer 1

$Answer -$

${v}^{2} = {u}^{2} + 2as$

$a = \frac{dv}{dt}$

$a = \frac{ds}{dt} \frac{dt}{ds}$

$a = v \frac{dv}{ds}$

$vdv = ads$

This is the third equation of motion.

In order to prove it by the method of calculus we need to integrate both sides of the equation with proper limits.

Refer to the attachment for further solution.

Answer 2

☺☺☺☺☺here is your answer OK



a=dv/dt

a =dv/dx * dx/dt (using chain rule)

since dx/dt=v

a= v dv/dx

a dx=v dv

a[dx]os =[v dv]uv

as=[v 1+1/2]uv

as=[v2/2]uv

as=v2-u2/2

therefore,

2as= v2-u2