Question

derive the following using velocity time graph a) v=u+at
b)s=ut+½at²
c)2as=v²-u²

plz step by step​

Answer 1

As We know the acceleration of body can be find using a = (v-u)/t.

From which we can derive Different Equations as well.

For 1st Equation:

→ a = (v-u)/t

→ at = v - u

→ v = u+at

For 2nd Equation:

• For Finding Average Velocity,

→ Average Velocity = (v+u)/2

• For Finding Final Displacement,

→ Displacement = Average Velocity × time

★ Displacement (s) = Ave. Velocity(v+u)/2 × time(t)

→ s = (v+u)/2 × t

→ s = (u+at+u)/2 × t

→ s = (2u+at)/2 × t

→ s = (2ut+at²)/2

→ s = ut + ½at²

For 3rd Equation:

We can derive third Equation of Motion using [1] and [2] Equation as well.

Firstly, We have eliminate Time (t) Formula from acceleration.

→ a = (v-u)/t

→ t = (v-u)/a

→ s = ut + ½at²

→ s = u (v-u)/a + ½ a{(v-u)/a}²

→ s = (uv-u²)/a + ½a{(v²+u²-2uv)/a²}

→ s = (uv-u²)/a+ ½{v²+u²-2uv}/a

→ s = (uv-u²)/a + {v²+u²-2uv}/2a

→ s = {2uv-2u² + v²+u²-2uv}/2a

→ 2as = v²-u²

Hence,

All the three Equation of Motion have been derived above.