An object travels North at #9 m/s# for #5 s# and then travels South at #6 m/s# for # 3 s#. What are the object's average speed and velocity?

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Answer 1 · 2018-07-22T15:34:14

average speed #\bar v=7.875\ \text{m/s#

velocity # v=6.058\ \text{m/s#

Average speed

#\bar v=\frac{\text{total distance traveled }}{\text{total time}}#

#=\frac{v_1t_1+v_2t_2}{t_1+t_2}#

#=\frac{9\times 5+6\times 3}{5+3}#

#=\frac{63}{8}#

#=7.875#

hence average speed #\bar v=7.875\ \text{m/s#

Velocity

#v=\frac{\text{displacement }}{\text{total time}}#

#=\frac{\sqrt{(v_1t_1)^2+(v_2t_2)^2}}{t_1+t_2}#

#=\frac{\sqrt{(9\times 5)^2+(6\times 3)^2}}{5+3}#

#=\frac{9\sqrt{29}}{8}#

#=6.058#

hence the velocity # v=6.058\ \text{m/s#