Question

Derive
$\sf{x = ut + \frac{1}{2}at {}^{2} }$

By calculus method

Class 11 physics ​

Answer 1

Answer:

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Answer 2

Actually,Welcome to the concept of Kinematics:-

First, we have to tak,e the following assumptions .

Let a body moves with constant acceleration by initial velocity "u" after time "t" it velocity becomes "v".

then,

v→ = $\frac{ds}{dt}$

integrate on both sides.

∫ ds = ∫ vdt

now put limits,

use v = u + at

0 to s ∫ ds = 0 to t ∫ (u + at) dt

0 to s ∫ ds = 0 to t ∫ + 0 to t∫ at. dt

[S] 0 to s = u[t] 0 to t + a 0 to t∫ t. dt

$s = ut + a \frac{ {t}^{2} }{2}$

$s = ut + \frac{1}{2} a {t}^{2}$

hence, proved.

0 to s and 0 to t are limits used here.

For more see attachment.