Derive the following equation for a uniformly accelerated motion:

$v = u + a t$

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Solution

Consider the linear motion of a body with an initial velocity 𝑢. It accelerates uniformly and in time 𝑡, it acquires the final velocity 𝑣. Velocity-time graph of the body will be a straight line 𝐴𝐵 as shown in the graph.

From the graph,
Initial velocity $(a t t = 0) = O A = u$
Final velocity $(a t t i m e t) = O E = v$

We know that the slope of velocity-time graph will give acceleration.
Acceleration = Slope of line AB $= \frac{D B}{A D} = \frac{A E}{O C}$
$= \frac{O E - O A}{O C} = \frac{v - u}{t}$
$a = \frac{v - u}{t}$
$a t = v - u$
$v = u + a t$

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Similar questions

Derive following equations for a uniformly accelerated motion :

(i) v=u+at

(ii) $S = u t + \frac{1}{2} a t^{2}$

(iii) $v^{2} = u^{2} + 2 a S$

where the symbols have their usual meanings.

v = u + a t

v^{2} = u^{2} + 2 a s

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