Question

3. Derive the equation = u + at of an object moving with
uniform acceleration on a linear path.
give me the pics​

Answer 1

hi there,

We know,

a = V-u/t

at=V-u

V = u +at

V : Final velocity

u: initial vel.

t: time

Answer 2

Derivation by Calculus Method :

Instantaneous acceleration, $\mathsf{a \:=\:{\dfrac{dv} {dt}}}$

$\mathsf{adt \:=\:dv}$

Integrating between the limit - initial time = 0

Intitial velocity = u, final time = t, final velocity = v

$\displaystyle a \int\limits_{0}^{t} dt = \int\limits _{u} ^{v} dv$

$\mathsf{a(\:t\:-\:0\:)\:=\:v\:-\:u}$

$\mathsf{at\:=\:v\:-\:u}$

$\implies{\boxed {\mathsf{v\:=\:u\:+\:at}}}$

By Graphical Method :

Let a body is moving with a velocity ' u ' with uniform acceleration after time ' t ', velocity of body becomes ' v' and distance travelled is ' s '.

From velocity  - time graph,

Slope of v-t graph = Acceleration of the body

$\implies{\mathsf{a\:=\:{\dfrac{BC} {AC}} \:=\:{\dfrac{OE\:-\:OA} {OD}}}}$

$\implies{\mathsf{a\:=\:{\dfrac{v\:-\:u} {t}}}}$

$\implies{\mathsf{at\:=\:v\:-\:u}}$

$\boxed{\mathsf{v\:=\:u\:+\:at}}$