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Shkiper50 [21]
3 years ago
11

Joe drove at the speed of 45 miles per hour for a certain distance. He then drove at the speed of 55 miles per hour for the same

distance. What is the average speed for the whole trip?
Physics
2 answers:
Oksi-84 [34.3K]3 years ago
8 0

Answer:

47.37 miles per hour,

Explanation:

The average speed is given by the formula

Average speed =(total distance / total time)

Let the distance Joe traveled at a speed of 45 miles per hour be 'D', because he then drove the same distance with a speed of 50 miles per hour then, the total distance is '2D'.

The total time will be the time he drove at a speed of 45 miles per hour (t_{1}) plus the time he drove at a speed of 50 miles per hour (t_{2}).

Then the average speed is :

v_{average} = \frac{2D}{t_{1}+t_{2}}.

Because we know that uniform rectilinear motion is discribed by the ecuation

d=\v*t (where d is distance, v is a constant speed and, t is the time)

we can express both times in terms of speeds and the distance, thus

t_{1} =\frac{D}{v_{1}} and,

t_{2} =\frac{D}{v_{2}}.

So now the average speed v_{average} = \frac{2D}{t_{1}+t_{2}} can be written as follows:

v_{average} = \frac{2D}{(\frac{D}{v_{1}}+\frac{D}{v_{2}} )}

v_{average} = \frac{2D}{D(\frac{1}{v_{1}}+\frac{1}{v_{2}} )}

v_{average} = \frac{2}{(\frac{1}{v_{1}}+\frac{1}{v_{2}} )}

v_{average} = \frac{2}{(\frac{1}{45}+\frac{1}{50} )}

v_{average} = 47.37 miles per hour.

Snowcat [4.5K]3 years ago
5 0

Answer:

v_{avg} = 49.5 mph

Explanation:

Let the distance moved by Joe is "d"

so the time taken by him to drove it by speed 45 mph is given as

t_1 = \frac{d}{v_1}

t_1 = \frac{d}{45}

now the same distance is traveled by him with speed 55 mph

so the time taken by him

t_2 = \frac{d}{55}

so total time taken by him for complete distance 2d

t = t_1 + t_2

t = \frac{d}{45} + \frac{d}{55}

t = 0.0404 d

now the average speed is given as

v_{avg} = \frac{2d}{t}

v_{avg} = \frac{2d}{0.0404d}

v_{avg} = 49.5 mph

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