An object travels North at # 6 m/s# for #8 s# and then travels South at # 3 m/s# for # 7 s#. What are the object's average speed and velocity?

1 Answer
Mar 17, 2018

Answer:

Average speed #"= 4.6 m/s"#

Average velocity #"= 1.8 m/s along North"#

Explanation:

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

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

#<< V >> = (("6 m/s × 8 s") + ("3 m/s × 7 s"))/("8 s + 7 s") = color(blue)"4.6 m/s"#


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

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

#<< vecV >> = (("6 m/s" (hatj) × "8 s") + ("3 m/s" (-hatj) × "7 s"))/("8 s + 7 s")#

#<< vecV >> = (48hatj - 21hatj)/15\ "m/s"#

#<< vecV >> = (27 hatj)/15\ "m/s" = 1.8hatj\ "m/s" = color(blue)"1.8 m/s along North"#