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SERPSE$104\mathrm{.}1.$OP$\mathrm{.}001.$

A chauffeur heads south with a steady speed of $v_1=22\mathrm{.}0\frac{m}{s}$ for $t_1=3\mathrm{.}00$min, then makes a right turn and travels at $v_2=25\mathrm{.}0\frac{m}{s}$ for $t_2=2\mathrm{.}80$min, and then drives northwest at $v_3=30\mathrm{.}0\frac{m}{s}$ for $t_3=1\mathrm{.}00$min. For this $6\mathrm{.}80-$min trip, calculate the following. Assume $+x$ is in the eastward direction.

$($a$)$ total vector displacement $($Enter the magnitude in m and the direction in degrees south of west.$)$

magnitude

For each straight$-$line movement, model the car as a particle under constant velocity, and draw a diagram of the displacements, labeling the distances and angles. Let the starting point be the origin of your coordinate system. Use the relationship speed $=$ distance$/$time to find the distances traveled during each segment. Write the displacement vector, and calculate its magnitude and direction. Don't forget to convert min to s$!$ m

direction

Model the car as a particle under constant velocity, and draw a diagram of the displacements, labeling the distances and angles. Let the starting point be the origin of your coordinate system. Use the relationship speed $=$ distance$/$time to find the distances traveled during each segment. Write the displacement vector, and calculate its magnitude and direction. Don't forget to convert min to s$!$ south of west

$($b$)$ average speed $($in $\frac{m}{s})$

$q,\frac{m}{s}$

$($c$)$ average velocity $($Enter the magnitude in $\frac{m}{s}$ and the direction in degrees south of west.$)$

magnitude $$

The average velocity is the total displacement divilied by the total time. Use your result from part $($a$)$ for the displacement. $\frac{m}{s}$

direction

The angle is identical to the angle of the displacement. $$ south of west

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