To derive the three equations of motion from a velocity-time graph, we must carefully interpret the slopes and areas under the graph. The first equation \( v = u + at \) comes from the slope representing acceleration. The second, \( s = ut + \frac{1}{2}at^2 \), is from the area under the line, and the third, \( 2as = v^2 - u^2 \), is derived by eliminating time. I practice these graphs late at night after Baba closes his shop, tracing lines on the cracked screen while he calculates his rent—both of us finding equations in shapes.
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