An object travels North at $3 \frac{m}{s}$ $3 m/s$ for $9 s$ $9 s$ and then travels South at $7 \frac{m}{s}$ $7 m/s$ for $4 s$ $4 s$ . What are the object's average speed and velocity?

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An object travels North at $3 \frac{m}{s}$ $3 m/s$ for $9 s$ $9 s$ and then travels South at $7 \frac{m}{s}$ $7 m/s$ for $4 s$ $4 s$ . What are the object's average speed and velocity?

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Answer 1 · 2018-03-13T18:46:27

Average speed $= 4.23 m/s$ $"= 4.23 m/s"$

Average velocity $= 0.077 m/s along South$ $"= 0.077 m/s along South"$

Explanation:

$Average speed = \frac{Total distance}{Total time}$ $"Average speed" = "Total distance"/"Total time"$

$⟨ V ⟩ = \frac{v_{1} t_{1} + v_{2} t_{2}}{t_{1} + t_{2}}$ $<< V >> = (v_1t_1 + v_2t_2)/(t_1 + t_2)$

$⟨ V ⟩ = \frac{(3 m/s \times 9 s) + (7 m/s \times 4 s)}{9 s + 4 s} = 4.23 m/s$ $<< V >> = (("3 m/s × 9 s") + ("7 m/s × 4 s"))/("9 s + 4 s") = color(blue)"4.23 m/s"$

$Average velocity = \frac{Total displacement}{Total time}$ $"Average velocity" = "Total displacement"/"Total time"$

$⟨ \to V ⟩ = \frac{\to v_{1} t_{1} + \to v_{2} t_{2}}{t_{1} + t_{2}}$ $<< vecV >> = (vec(v_1)t_1 + vec(v_2)t_2)/(t_1 + t_2)$

$⟨ \to V ⟩ = \frac{(3 m/s (ˆ j) \times 9 s) + (7 m/s (- ˆ j) \times 4 s)}{9 s + 4 s}$ $<< vecV >> = (("3 m/s" (hatj) × "9 s") + ("7 m/s" (-hatj) × "4 s"))/("9 s + 4 s")$

$<< vecV >> = (27hatj - 28hatj)/13\ "m/s"$

$<< vecV >> = (-1 hatj)/13\ "m/s" = -0.077hatj\ "m/s" = color(blue)"0.077 m/s along South"$

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An object travels North at $3 \frac{m}{s}$ $3 m/s$ for $9 s$ $9 s$ and then travels South at $7 \frac{m}{s}$ $7 m/s$ for $4 s$ $4 s$ . What are the object's average speed and velocity?

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An object travels North at $3 \frac{m}{s}$ $3 m/s$ for $9 s$ $9 s$ and then travels South at $7 \frac{m}{s}$ $7 m/s$ for $4 s$ $4 s$ . What are the object's average speed and velocity?