An object travels North at # 3 m/s# for #9 s# and then travels South at # 7 m/s# for # 4 s#. What are the object's average speed and velocity?

1 Answer
Mar 13, 2018

Answer:

Average speed #"= 4.23 m/s"#

Average velocity #"= 0.077 m/s along South"#

Explanation:

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

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

#<< V >> = (("3 m/s × 9 s") + ("7 m/s × 4 s"))/("9 s + 4 s") = color(blue)"4.23 m/s"#


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

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

#<< vecV >> = (("3 m/s" (hatj) × "9 s") + ("7 m/s" (-hatj) × "4 s"))/("9 s + 4 s")#

#<< vecV >> = (27hatj - 28hatj)/13\ "m/s"#

#<< vecV >> = (-1 hatj)/13\ "m/s" = -0.077hatj\ "m/s" = color(blue)"0.077 m/s along South"#