Derive the first equation of motion (v = u + at) graphically.

PROMPT: A velocity-time graph showing uniform acceleration. The y-axis represents velocity (v) and the x-axis represents time (t). A straight line starts from initial velocity 'u' on the y-axis at t=0 and goes up to final velocity 'v' at time 't'. A horizontal dashed line extends from 'u' to the point (t,u) and a vertical dashed line extends from 'v' to the point (t,v). A point 'A' is at (0,u), 'B' is at (t,v), 'C' is at (t,u), and 'D' is at (0,0). The slope of the line AB represents acceleration.

Consider an object moving with uniform acceleration 'a'. Let its initial velocity be 'u' at time t=0, and its final velocity be 'v' at time 't'.
From the velocity-time graph, acceleration is the slope of the velocity-time graph.
Slope = (Change in velocity) / (Change in time)
a = (v - u) / (t - 0)
a = (v - u) / t
at = v - u
Therefore, v = u + at.