An object travels North at #9 m/s# for #2 s# and then travels South at #7 m/s# for # 6 s#. What are the object's average speed and velocity?
1 Answer
Answer:
Average speed:
Average velocity:
Explanation:
We're asked to find an object's average speed and average velocity with a given displacement.
Let's find the average velocity first:
The object is moving in one dimension (which since it's north and south, we'll call the
The formula for the average velocity (along the
where

#Deltay# is the total change in#y# position, and 
#Deltat# is the change in time, which is#2# #"s"# #+ 6# #"s" = color(red)(8# #color(red)("s"#
We therefore need to find the total change in position,
For the first displacement (north), the distance traveled is
And the second displacement (south) is
(negative because we're calling south the negative direction.)
The net displacement is
The average velocity is thus
Now, let's find the average speed:
The average speed of an object is
The total distance traveled is the sum of the two displacements, disregarding the signs.
It traveled
The time interval is the same, so the average speed is
(It's always helpful to know that average speed is always a positive value, since we're only dealing with the magnitudes of the displacements, not the directions/signs.)