An object travels North at #1 m/s# for #8 s# and then travels South at #6 m/s# for # 4 s#. What are the object's average speed and velocity?

1 Answer
Apr 8, 2017

Answer:

Average speed: #2 2/3 m/scolor(white)("XXX")#Average velocity: #1 1/3 m/s ["South"]#

Explanation:

The object travels:
#color(white)("XXX")#North: #1 m/s xx 8 s =8 m#
#color(white)("XXX")#South: #6 m/s xx 4 s =24 m#

For a total distance of #32 m#
and
#color(white)("XXX")#(noting that #24 m" South" = -24 m" North"#)
a resulting displacement of #8 m (N) - 24 m (N)=-16 m (N)#

Total travel time: #8 s + 4 s = 12 s#

Average speed #= ("total distance")/("total time")= (32 m)/(12 s)=2.66bar6 m/s#

Average velocity#=("resulting displacement")/("total time")=(-16 m "(N)")/(12 s)=-1.33bar3 m/s "(N)"#

#color(white)("XXX")#or#color(white)("XXXXXXXXXXXXXXXXXXXXXX")+1.33bar3 m/s "(S)"#

Notice that displacement and velocity should always contain a component indicating direction.