Final answer:
Speed is the rate of change of position, while velocity is rate of change of position with direction. Hence the average speed of a ball returning to its starting point can be greater than its average velocity (which would be zero in this case). Slope on a velocity-time graph represents acceleration, and a position-time graph of a speeding up object is curved.
Step-by-step explanation:
When discussing speed and velocity in physics, it is important to note the difference between the two. Speed is the scalar quantity that refers only to the rate of change of position, whereas velocity is a vector quantity that refers to the rate of change of position in a given direction. Therefore, if a ball's path takes it back to its starting point, its displacement is zero, and hence the average velocity is also zero, since velocity is based on displacement, not distance covered. However, the average speed, which is total distance divided by time, could be greater than zero.
In the case of a car moving on a straight road at a constant speed, since there is no change in speed or direction, the velocity is also constant, and thus the car’s speed equals its velocity. If you take the slope of the velocity vs. time graph for the jet car, it will give you the acceleration of the jet car, not the velocity. Acceleration refers to the rate of change of velocity. If the slope is constant, then the acceleration is constant. A position vs time graph of an object that is speeding up is not a straight line but rather a curve that gets steeper over time.
In relation to Kepler's laws, it is indeed true that a satellite increases its speed as it approaches the parent body due to gravitational pull and decreases as it moves away. As for the comet, relativistic effects regarding its tail are not typically a factor for an observer on Earth and such effects are usually negligible for the speeds comets have in our solar system.