A body moving with a constant acceleration a possesses some initial velocity u.What will be its velocity after it has covered certain distance S ?

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Solution

Step 1: Assumption
Given that
A body is moving with a constant acceleration = a
Initial velocity is u.
Let the time be t.
Step 2: Calculation
The velocity of the body after it has covered a certain distance S is v.
We know that
$v = u + a t$ (Squaring this equation)
$v^{2} = {(u + a t)}^{2} . v^{2} = u^{2} + 2 u a t + a^{2} t^{2} v^{2} = u^{2} + 2 a (u t + \frac{1}{2} a t^{2})$
We know that $S = u t + \frac{1}{2} \times a \times t^{2}$
$v^{2} - u^{2} = 2 a s$
$v^{2} = u^{2} + 2 a s$
$v = \sqrt{u^{2} + 2 a s}$
The velocity of the body after it has covered a certain distance S is $v = \sqrt{u^{2} + 2 a s} .$

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