Final answer:
A speed-time graph's slope indicates acceleration. At 40 minutes, the slope determines acceleration, which is constant for a linear graph. An acceleration-time graph shows changes in speed over time.
Step-by-step explanation:
The feature of a speed-time (or velocity-time) graph that shows acceleration is the slope of the graph. A straight line with a non-zero slope indicates constant acceleration, while a curved line indicates changing acceleration. To find the acceleration of a person at a specific time, such as 40 minutes, you would need to look at the slope of the graph at that point. If the graph is linear and the slope is constant, the acceleration would also be constant. If the graph has a curve, the acceleration is changing, and you can determine the instantaneous acceleration by taking the derivative of the velocity with respect to time at that particular point.
A graph of acceleration vs. time helps to understand how an object's speed changes over time. For a constant acceleration, this graph would show a horizontal line, representing the unchanging rate of speed increase or decrease. When acceleration is zero, the graph will show a flat horizontal line, indicating no change in speed. If the acceleration varies over time, the graph will have a different shape, such as a curve, to reflect the changing rates.