An object travels North at $9 \frac{m}{s}$ $9 m/s$ for $5 s$ $5 s$ and then travels South at $6 \frac{m}{s}$ $6 m/s$ for $3 s$ $3 s$ . What are the object's average speed and velocity?

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Answer 1 · 2018-07-22T15:34:14

average speed $\bar v=7.875\ \text{m/s$

velocity $v=6.058\ \text{m/s$

Average speed

$\bar v=\frac{\text{total distance traveled }}{\text{total time}}$

$=\frac{v_1t_1+v_2t_2}{t_1+t_2}$

$=\frac{9\times 5+6\times 3}{5+3}$

$=\frac{63}{8}$

$=7.875$

hence average speed $\bar v=7.875\ \text{m/s$

Velocity

$v=\frac{\text{displacement }}{\text{total time}}$

$=\frac{\sqrt{(v_1t_1)^2+(v_2t_2)^2}}{t_1+t_2}$

$=\frac{\sqrt{(9\times 5)^2+(6\times 3)^2}}{5+3}$

$=\frac{9\sqrt{29}}{8}$

$=6.058$

hence the velocity $v=6.058\ \text{m/s$

An object travels North at 9 m/s9ms9 m/s for 5 s5s5 s and then travels South at 6 m/s6ms6 m/s for 3 s3s 3 s. What are the object's average speed and velocity?