Question

which graph shows acceleration? position (m) time (s) position (m) time (s) position (m) time (s)

Explanation:

Step1: Recall motion graphs

In position - time graphs, the slope represents velocity. For acceleration to be non - zero, the velocity (slope) must be changing.

• For the first graph (straight line from origin): The slope is constant, so velocity is constant (no acceleration, uniform motion).
• For the second graph (curved, upward - bending): The slope of the position - time graph is increasing (as we move along the time axis, the steepness of the curve increases). Since slope = velocity, an increasing slope means increasing velocity, which implies acceleration (because acceleration is the rate of change of velocity).
• For the third graph (straight line decreasing from a peak): The slope is constant (negative slope, constant velocity in the opposite direction, no acceleration).

Step2: Identify the accelerating graph

From the above analysis, the second graph (the curved position - time graph) has a changing slope (changing velocity), so it represents motion with acceleration.

Answer:

The second graph (the one with the upward - curving position - time plot)