Question

An object travels North at `8 m/s` for `6 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 `"= 7.6 m/s"`

Average velocity `"= 2 m/s along North"`

Explanation:

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

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

`<< V >> = (("8 m/s × 6 s") + ("7 m/s × 4 s"))/("6 s + 4 s") = color(blue)"7.6 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 >> = (("8 m/s" (hatj) × "6 s") + ("7 m/s" (-hatj) × "4 s"))/("6 s + 4 s")`

`<< vecV >> = (48hatj - 28hatj)/10 "m/s"`

`<< vecV >> = (20 hatj)/10 "m/s" = 2hatj "m/s" = color(blue)"2 m/s along North"`

Answer 2

`"Average speed" = 7.6 m/s` and `"Average velocity" = 2.0 m/s`

Explanation:

The distance North, `s_n`, it traveled during that first part was

`s_n = v_n*t_n = 8 m/s*6 s = 48 m`

The distance Sorth, `s_s`, it traveled during that first part was

`s_s = v_s*t_s = 7 m/s*4 s = 28 m`

Average speed

`"Average speed " = "total distance"/"total time" " "` So, plugging in our data,

`"Average speed " = (48 m + 28 m)/(6 s + 4 s) = (76 m)/(10 s)`
`"Average speed" = 7.6 m/s`

Average velocity

`"Average velocity " = "total displacement"/"total time"`
To determine displacement, we need a rule for what the positive direction is. I declare that North is the positive direction. So, plugging in our data,

`"Average velocity" = (48 m - 28 m)/(6 s + 4 s) = (20 m)/(10 s)`
`"Average velocity" = 2.0 m/s`

I hope this helps,
Steve