Question

Derive all the three equations of motion for uniform acceleration using graphical method.​

Answer 1

Answer:

Explanation: Three equation of motion can be derives as,

For graphical method we need experimental points so you have to insert the points. Here I have derives the equations analytically.

When acceleration (a) is constant for a moving body then,

we have,  $\frac{dv}{dt}$ = constant = a  ; where v is the velocity at time t.

so, v = at + c

Now if we take v = u at time t = 0 then we have v = u + at   (1)

Next we know, $v = \frac{ds}{dt}$ ;  where s is the displacement of the body at time t.

so, $\frac{ds}{dt} = u + at$

or,  $s = ut + \frac{1}{2} a t^{2}$   (2)

Again,  $a = \frac{dv}{dt} = \frac{ds}{dt} \frac{dv}{ds} = v \frac{dv}{ds}$

so,                            

$a ds = vdv \\\\or, \int_0^s a ds = \int_u^v v dv \\\\or, a s = \frac{v^2}{2} - \frac{u^2}{2} \\\\or, v^2 = u^2 +2a s$    (3)