Final answer:
A u-shaped position-time graph depicts variable acceleration, indicating that the object is first decelerating and then accelerating as it follows the curved trajectory.
Step-by-step explanation:
If you draw a velocity-time graph and use the slope to determine acceleration, a u-shaped position-time graph indicates variable acceleration. In the initial part of the u-shaped curve where the graph curvature is upwards, the object is decelerating, as indicated by a negative slope if this were translated to a velocity-time graph. Once the curve reaches its lowest point and begins to curve upwards, the acceleration becomes positive, indicated by an upwards slope in the velocity-time graph. Therefore, the object experiences variable acceleration, changing from negative to positive as it moves through the trajectory described by the u-shaped position-time graph.