Question

You drive due east down a perfectly straight freeway for 39 minutes at 0.8 miles per minute. Then you get off at a rest stop and have lunch, which takes 28 minutes. Then you get back on the freeway, which is still perfectly straight, and drive for another 54 minutes at 0.9 miles per minute in the same direction (east). The length of the on and off ramps, and the distance to the rest stop, are very small and should be ignored. What is your average velocity, to the nearest 0.1 mile per minute, for the entire trip?

Answer #1

v_{1} = initial velocity in east direction = 0.8 miles
per min

t_{1} = 39 min

d_{1} = distance travelled in first case in east
direction = v_{1} t_{1} = 0.8 x 39 = 31.2 miles

v_{2} = initial velocity in east direction = 0.9 miles
per min

t_{2} = 54 min

d_{2} = distance travelled in second case in east
direction = v_{2} t_{2} = 0.9 x 54 = 48.6 miles

D = total distance travelled = d_{1} + d_{2} =
31.2 + 48.6 = 79.8 miles

t = total time = t_{1} + t_{2} + 28 = 39 + 54 +
28 = 121 min

average velocity is given as

V = D/t

V = 79.8/121

V = 0.7 miles/min

A small radio transmitter broadcasts in a 39 mile radius. If you
drive along a straight line from a city 49 miles north of the
transmitter to a second city 54 miles east of the transmitter,
during how much of the drive will you pick up a signal from the
transmitter?

You start out by driving 107 miles north in 2 hours and 20
minutes, and then you stop and park for a while. Finally you drive
another 54 miles south in 2 hours and 6 minutes. The average
velocity for your entire trip was 29.05 miles per hour to the
south. How much time did you spend parked?
a) 2 hours 12 minutes
b) 0 hours 33 minutes
c) 5 hours 32 minutes
d) 1 hour 6 minutes

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