1.

Derive:​

Answer»

Answer:

To derive :

2nd Equation of motion USING graphical methods.

s = ut + ½at²

Proof:

Lets CONSIDER a velocity-time graph as attached above.

Now we know that displacement is given by the area under the velocity time graph.

Let initial velocity be u , final velocity be v , acceleration be a , time be t and distance be s

Now, area under the curve:

∴ s = Area of the trapezium

=> s = ½ (SUM of parallel sides) × DIST. between them

=> s = ½ (u + v ) × t ......(1)

Now we know that :

v = u + at .....(from 1ST eq. of motion) ......(2)

So putting value of "v" in eq.(1)

∴ s = ½ { u + (u + at)} × t

=> s = ½ { 2u + at } × t

=> s = ut + ½at²

[Hence proved .]


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