Question

Drive the equation of motion V square subtractor square you square is equal to 2 a s using graphical method

Answer 1

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• u = Initial velocity
• v = Final velocity
• s = distance travelled
• t = time taken
• a = acceleration

• The distance (s) travelled by the object in the time (t), moving under uniform acceleration (a) is given by the area of the figure
• OPNR is a trapezium.(see fig. above in attachment)

Distance travelled, s = Area of trapezium OPNR

$s = \frac{(sum \: of \: parallel \: sides) \times height}{2}$

$s = \frac{(OP + NR) \times OR}{2}$

Now, OA + CB = u + v

and

OC = t

• Putting these values in the above relation, we get :

$s = \frac{(u + v) \times t}{2}$

• Using First equation of motion

$v = u + at \\ \\ at = v - u \\ \\ t = \frac{(v - u)}{a}$

• Putting these value of t in equation above :

$s = \frac{(u + v) \times(v - u) }{2a}$

or

$2as = {v}^{2} - {u}^{2}$

because [(v + u) × (v - u) = v² - u²]

${v}^{2} = {u}^{2} + 2as$

$\huge\mathcal\colorbox{red}{{\color{aqua}{Hope \: it \: is \: helpful}}}$

Answer 2

Explanation:

Hope it helps you....

Have a nice day...