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?

Question

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?

Amelia Adams · Accepted Answer

Average speed #"= 4.23 m/s"#

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

Isabella Alvarez · Answer

undefined Average speed: \( \frac{{\text{{total distance}}}}{{\text{{total time}}}} = \frac{{(3 \, \text{m/s} \times 9 \, \text{s}) + (7 \, \text{m/s} \times 4 \, \text{s})}}{{9 \, \text{s} + 4 \, \text{s}}} = \frac{{(27 \, \text{m}) + (28 \, \text{m})}}{{13 \, \text{s}}} = \frac{{55 \, \text{m}}}{{13 \, \text{s}}} \approx 4.23 \, \text{m/s}$.

Average velocity: \( \frac{{\text{{total displacement}}}}{{\text{{total time}}}} = \frac{{(3 \, \text{m/s} \times 9 \, \text{s}) - (7 \, \text{m/s} \times 4 \, \text{s})}}{{9 \, \text{s} + 4 \, \text{s}}} = \frac{{(27 \, \text{m}) - (28 \, \text{m})}}{{13 \, \text{s}}} = \frac{{-1 \, \text{m}}}{{13 \, \text{s}}} \approx -0.08 \, \text{m/s}$ north.