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?

Answer 1

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"`

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`"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"`