Which one of the following graphs represents the equation of motion v = u + at; where all quantities are non-zero and symbols carry their usual meanings ?

The equation v = u + at describes motion with constant acceleration. When representing this motion on a distance-time (s-t) graph, we use the second equation of motion: s = ut + ½at².

• Non-zero acceleration (a): Since acceleration is non-zero, the velocity (slope of the s-t graph) changes over time. This results in a parabolic curve rather than a straight line.
• Non-zero initial velocity (u): Since u is non-zero, the graph starts with a definite positive slope at t = 0, meaning the object is already in motion.
• Linear vs. Quadratic: A straight line on a distance-time graph represents constant velocity (zero acceleration). Therefore, to represent v = u + at where a ≠ 0, the distance-time graph must be a curve.

Option D correctly depicts this parabolic relationship, showing that distance increases non-linearly as the object accelerates.