Interpreting Position-time Graphs

On a position-time graph the instantaneous velocity is given by the slope of the tangent to the curve at any instant. If the slope itself increases continuously with time, then the velocity is increasing with time, which by definition means the body has a positive acceleration. A curve that bends upward with an ever-steepening tangent therefore represents accelerated motion. The option 'constant velocity' is wrong because a uniform velocity would appear as a straight line of fixed slope, not a curve. The option 'at rest' is wrong because a stationary body produces a horizontal line of zero slope, indicating no change in position. The option 'decelerating to a stop' is wrong because slowing down would show a curve whose slope decreases and flattens, the opposite of the steepening trend described. This relies on the NCERT principle that the gradient of a position-time graph encodes velocity, and the rate at which that gradient itself changes encodes acceleration. Graphically, the curvature of the position-time plot is therefore a direct visual signature of acceleration, with upward concavity meaning positive acceleration and downward concavity meaning negative acceleration. As a consistency check, a steepening position-time curve must correspond to a rising velocity-time line, both signalling the same underlying accelerated motion.