An object travels North at # 8 m/s# for #6 s# and then travels South at # 7 m/s# for # 4 s#. What are the object's average speed and velocity?

2 Answers
Mar 12, 2018

Answer:

Average speed #"= 7.6 m/s"#

Average velocity #"= 2 m/s along North"#

Explanation:

#"Average speed" = "Total distance"/"Total time"#

#<< V >> = (v_1t_1 + v_2t_2)/(t_1 + t_2)#

#<< V >> = (("8 m/s × 6 s") + ("7 m/s × 4 s"))/("6 s + 4 s") = color(blue)"7.6 m/s"#


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

#<< vecV >> = (vec(v_1)t_1 + vec(v_2)t_2)/(t_1 + t_2)#

#<< vecV >> = (("8 m/s" (hatj) × "6 s") + ("7 m/s" (-hatj) × "4 s"))/("6 s + 4 s")#

#<< vecV >> = (48hatj - 28hatj)/10 "m/s"#

#<< vecV >> = (20 hatj)/10 "m/s" = 2hatj "m/s" = color(blue)"2 m/s along North"#

Mar 12, 2018

Answer:

#"Average speed" = 7.6 m/s# and #"Average velocity" = 2.0 m/s#

Explanation:

The distance North, #s_n#, it traveled during that first part was

#s_n = v_n*t_n = 8 m/s*6 s = 48 m#

The distance Sorth, #s_s#, it traveled during that first part was

#s_s = v_s*t_s = 7 m/s*4 s = 28 m#

Average speed

#"Average speed " = "total distance"/"total time" " "# So, plugging in our data,

#"Average speed " = (48 m + 28 m)/(6 s + 4 s) = (76 m)/(10 s)#
#"Average speed" = 7.6 m/s#

Average velocity

#"Average velocity " = "total displacement"/"total time"#
To determine displacement, we need a rule for what the positive direction is. I declare that North is the positive direction. So, plugging in our data,

#"Average velocity" = (48 m - 28 m)/(6 s + 4 s) = (20 m)/(10 s)#
#"Average velocity" = 2.0 m/s#

I hope this helps,
Steve