SOLUTION: A car travels at 60 mph east for 20 min then at 30 mph north for 30 min. What is the average speed and average velocity?

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Question 350545: A car travels at 60 mph east for 20 min then at 30 mph north for 30 min. What is the average speed and average velocity?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate*Time=Distance
R%2At=D
Find the total distance traveled.
60%281%2F3%29=20 miles East
30%281%2F2%29=15 miles North
D%5Bt%5D=20%2B15
D%5Bt%5D=35miles
Find the total time elapsed,
t=1%2F3%2B1%2F2=5%2F6hr
Average speed is distance traveled divided by time elapsed.
V%5Bave%5D=35%2F%286%2F5%29=42mph
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.
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Average velocity is the change in the position vector divided by elapsed time.
(0,0) is the starting point.
East is positive x.
North is positive y.
Determine the final position.
(0,0)+(20,0)+(0,15)=(20,15)
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The magnitude of the position vector is V%5E2=20%5E2%2B15%5E2=625
abs%28X%29=25 miles
Divide by elapsed time,
abs%28V%29=25%2F%285%2F6%29
abs%28V%29=30 mph
The direction is given by
tan%28theta%29=15%2F20 where theta is the angle measured CCW from the x-axis.
theta=36.9 degrees
The velocity vector has magnitude 30 mph and angle of 36.9+degrees or in vector coordinates (24,18) mph.