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An object travels North at #6 m/s# for #5 s# and then travels South at #7 m/s# for # 5 s#. What are the object's average speed and velocity?

Answer 1

Average speed #=6.5m/s#
Average velocity# = -0.5m/s#

Average # "velocity" = "displacement"/"time elapsed"# #bar v = (Deltax)/(Delta t) # Average # "speed" = "distance traveled"/"time elapsed"# #bar s = d/(Delta t) #

Going north at 6m/s for 5s is 30m, and going south at 7m/s for 5s is 35m, hence the object in 10s has effectively gone south for 5m as a displacement despite it has actually traveled a total distance of 65m.

Bear in mind that for displacement going north is positive, south negative:

#Delta x = 6m/s*5s - 7m/s*5s= 30m-35m= - 5m#

#d = 30m + 35m = 65 m#

#Delta t = 5s+5s = 10s#

#bar v = (Deltax)/(Delta t) =-(5m)/(10s) = -0.5m/s # #bar s=d/(Delta t)=(65m)/(10s) = 6.5 m/s#

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Answer 2

Adrian Ayala

The object's average speed is 6.5 m/s, and its average velocity is 0 m/s.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.