Question

establish the formula :- S = ut +1/2 at², where the symbols have usual meaning​

Answer 1

Answer

If S is the displacement of the body during time t then,

Displacement = Avg. velocity × Time

$\sf S = (\frac{u+v}{2})t$

Substituting the value of v = u + at in the equation :-

⟹ $\sf S = [\frac{u+(u+at)}{2}] \times t$

⟹ $\sf S = [2u + at] \times \frac{t}{2}$

⟹ $\sf S = ut + \frac{1}{2} at^2$

where

• s is distance travelled
• u is initial velocity
• t is time taken
• a is acceleration

Additional information :-

First equation of motion :-

• v = u + at

Third equation of motion :-

• v² = u² + 2as

Equation of Snth :-

• Snth = u + ½ ( 2n - 1 ) a