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?

2 Answers
Mar 12, 2018

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"


"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"

Mar 12, 2018

"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