Final answer:
By observing the steepness of the tangent lines on a velocity versus time graph increasing over time, you can conclude that an object is speeding up since this represents positive acceleration.
Step-by-step explanation:
You can tell that an object is speeding up by looking at the tangent lines on a velocity versus time graph. If the object is speeding up, the slope of the tangent lines at different points on the graph will become increasingly steep as time goes by. This indicates that the velocity is increasing over time. When you look at a position versus time graph, the tangents to the curve represent the instantaneous velocity at different points. If the car is speeding up, these tangent lines will show a steepening slope as well. Additionally, the slope of the velocity versus time graph indicates the acceleration of the object. A positive and increasing slope on a velocity versus time graph means the object's velocity is increasing, thus the acceleration is positive and the object is speeding up.