Physics
Physics
Problem
The position–time graph of a motorbike is a smooth curve that becomes progressively steeper as time increases. Two points on the graph are marked: point P at t = 1.0 s and point Q at t = 3.0 s. Which of the following comparisons of the bike’s instantaneous velocity at the two points is most accurate? a) b) c) The comparison cannot be determined from the graph d)Intuitive explanation
The key insight is recognizing that instantaneous velocity equals the slope of the position–time graph at that moment. Since the curve gets progressively steeper, the slope—and therefore the instantaneous velocity—increases over time. You need to compare the steepness (slope) at point P versus point Q: which tangent line is tilted more steeply? The later point, being further along a curve that's continuously getting steeper, will have a greater slope and thus a higher instantaneous velocity.
Intuitive explanation
The key insight is recognizing that instantaneous velocity equals the slope of the position–time graph at that moment. Since the curve gets progressively steeper, the slope—and therefore the instantaneous velocity—increases over time. You need to compare the steepness (slope) at point P versus point Q: which tangent line is tilted more steeply? The later point, being further along a curve that's continuously getting steeper, will have a greater slope and thus a higher instantaneous velocity.