The positions of two objects are
shown at one-second time intervals. Which object has the greater
difference between its greatest average speed over one second and its least average
speed over one second?
Recall that speed is a relationship
between time and distance. Since the time intervals for each
object are the same, this question can be answered simply by observing the distance
that each object travels in each time interval. Each dot or triangle in the first
diagram shows where the object was at each second. Hence, the differences in speed are
directly proportional to the distance traveled each second.
We are looking not just for the
greatest distance traveled by each object, but the greatest difference between
distances. To solve this problem for one
object, look at the smallest distance traveled then the greatest distance traveled
and find the difference then repeat this process for the second object. Whichever object has the greatest
difference in distance traveled is the answer.
You might find it easier to
visualize this problem by looking at the second diagram, where we represent each
object as a dot labeled with the time the object was in that position. Object A appears to travel the
greatest distance and therefore have its greatest speed between two to three
seconds. It covers the least distance
between zero and one and one and two seconds. See the difference in speeds in
Repeating this process for object
B, we see that it travels the greatest distance between one and two seconds. Similarly to object A, object B
travels the least distance between zero and one second. See the difference in speeds in
Finally, we can get our answer by
comparing the differences in speeds, as in this image. We see that the difference between
object A’s fastest and slowest speeds is greater than the difference between object
B’s fastest and slowest speeds. So the answer is object A.