derive the equation S= ut+ 1/2 at^2 by graphical method.
Answers
Heya,
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Graph acceleration vs. time: this is a VERY BORING GRAPH.
Now graph velocity vs. time, calculating the new value of v at each value of t by adding the area under the a vs. t graph for that time step. You should notice that this is a straight line passing through u at t=0.
Now graph displacement vs. time, doing for s what you just did for v. If you want to do this entirely without a calculator, use graph paper and count squares.
To demonstrate *purely graphically* that this creates your formula, observe that s=ut+(1/2)at^2 is the equation of a parabola with a directrix of s = (u^2-1)/2a. Plot this point and a line the same distance the other side of the origin and your graph should be on the locus of points equidistant from both.
Now weep for all the people who actually had to do this, then use calculus as follows:
Definition, a=d (v) / dt
Integrate, v = u + a*t
Definition, v = d (s) / dt
Integrate, s = u*t + 1/2*a*t^2 + C
Let s (0) = 0 thus C =0 thus s = u*t + 1/2*a*t^2 QED
__________________________________Hope it helps!
