To determine if an object has negative acceleration by looking at its position-time graph, you need to examine the curvature or shape of the graph.
Straight Line with Negative Slope: If the position-time graph is a straight line with a negative slope (downward sloping line), this indicates that the object is moving with a constant velocity in the negative direction. In this case, the object is not experiencing any acceleration.
Curved Line Concave Downward: If the position-time graph shows a curved line that is concave downward, it suggests that the object is experiencing negative acceleration. This means that the object is slowing down as time progresses. The steeper the curvature, the greater the negative acceleration.
Curved Line Concave Upward: On the other hand, if the position-time graph displays a curved line that is concave upward, it implies positive acceleration. This indicates that the object is speeding up as time passes.
By analyzing the shape of the position-time graph, you can infer whether the object has negative, positive, or zero acceleration. Remember that acceleration represents the rate of change of velocity, so a change in the slope or curvature of the position-time graph indicates a change in acceleration.