Question

derive the relations of three equations of motion. a) v = u + at b) s = ut + 1/2 at^2 c) v^2 = u^2 = 2as 2​

Answer 1

Solution :

$\tt v = u + at.$

We have,

$\tt\implies \vec{a} = \frac{ \Delta \: v}{ \Delta \: t} \\ \tt\implies \vec{a} = \frac{dv}{dt} \\ \tt dv = \vec{a} \: dt.$

$\tt\implies \int dv = \int a \: dt \\ \implies \int \limits _{u}^{v} dv = \int \limits _{0}^{t} a \: dt$

Here, acceleration be constant.

so,

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

$\tt\implies [v]_{u}^{v} = a[t]_{0}^{t}$

$\tt\implies v - u = a(t - 0) \\ \tt\boxed{ v = u + at.}$

Hance Proved.

Other part provide in attachment.

Some information :

• v= u + at.
• s = ut + 1/at².
• v² = u² + 2as.