An object travels North at # 2 m/s# for #1 s# and then travels South at # 4 m/s# for # 9 s#. What are the object's average speed and velocity?

1 Answer
Jun 26, 2017

Answer:

Average velocity = #"-"3.09..."ms"^-1 "south"#
Average speed = #3.45..."ms"^-1#

Explanation:

We will deal with speed first. Speed is how far something travels per second.

North - #"speed"*"time"="distance"; 2*1=2"m"#
South - #"speed"*"time"="distance"; 4*9=36"m"#

Total distance travelled = 2+36=38m
Total time = 2 + 9 = 11s

#"Average speed" = "total distamce"/"total time"#

#"Average speed" = 38/11 = 3.45..."ms"^-1#

Average velocity:

As average takes direction into accpunt as well, the north value will be taken as positive, and the south value as negative (opposite directions, think add and subtract).

North - #"velocity"*"time"="displacement"; 2*1=2"m"#
South - #"velocity"*"time"="displacement"; "-"4*9="-"36"m"#

Total displacement = 2-36=-34m
Total time = 2 + 9 = 11s

#"Average velocity" = "total displacement"/"total time"#

#"Average velocity" = "-"34/11 = -3.09..."ms"^-1#

As the value for average velocity is negative, and so is the inital south value, the average velocity is therefore #"-"3.09..."ms"^-1 "south"#.