Question

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?

Answer 1

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"`

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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 >> = (("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"`