Consider the following statement: If an object\'s displacement magnitude equals
ID: 1330922 • Letter: C
Question
Consider the following statement:
If an object's displacement magnitude equals the distance traveled for an interval, then the object's average velocity will equal its average speed for the interval.
a) Is this statement valid?
b) If you contend the statement is valid, how do you know?
c) If you contend the statement is invalid, what is wrong with it?
d) If the statement is invalid, restate it to give a valid statement.
e) Is the valid statement (the original or your revision) a conditional or bi-conditional? How do you know?
f) Would the following investigation test provide data to either support or contradict the valid hypothesis? Explain.
A person rides a bicycle 25 times in such a way that the distance traveled is different from the magnitude of the displacement and finds the average speed and velocity for each trip.
Explanation / Answer
a) This is a valid statement.
b)
Refer the above figure,
In this figure one can see, the object is moving in one direction from point A to B. In this case displacement is a straight line distance from A to B, which is equal to the distance travelled from A to B. Hence in this case,
displacement = distance
velocity= displacement / time elapsed
speed = distance / time elapsed
Since distance equal to the displacement gives magnitude of velocity = magnitude of speed.
Thus both have equal magnitudes.
e) The valid statement is a conditional that object must travel in a straight line path from initial point to final point. Because only then we will get displacement = distance.
f) the test here contradicts with the hypothesis because rider here moving from point a to B and then returning to point A again making displacement zero for each trip. So for each trip displacement is zero but distance goes on increasing as a result we get different magnitudes for displacement and distance quantities.
Here for each trip velocity = displacement/time elapsed = 0/t = 0 m/s
and speed = no. of trips* speed for a trip.