Question

Starting from a complete stop, a car gets on I-80 at the I-80 and I-680 interchange, then drives to Stuart and continues east. After starting to move, the car accelerates over a distance of 1/4 mile, until reaching 55 miles per hour and continuing to Stuart at that constant speed. So between the I-680 interchange and Stuart, the time and distance can be considered to be composed of two time/distance parts:

Google maps shows it is 65.5 miles from I680 to stuart

time(1): the time taken accelerating from 0 mph to 55 mph during the first 1/4 mile

distance(1): the first 1/4 mile over which the car was accelerating

time(2) the time taken to cover the rest of the distance to Stuart going at the constant speed 55 mph

distance(2): the rest of the distance to Stuart after the 1st 1/4 mile

5.A. What is distance(2), the distance to Staurt after the 1^st ¼ mile? _______________

5.B.   What is the time time(1) spent accelerating, in units of hours?___________

5.C. What is the time time(2) spent driving at the constant speed after the 1^st ¼ mile to Stuart? ____________

5.D. - What percentage of the total distance of the trip (distance(1) + distance(2)) between I-680 interchange and Stuart was spent accelerating?

5.E.   What percentage of the total time of this trip (time(1) + time(2)) was spent accelerating?

Answer 1

I have a doubt in distance...... is it 1/4 mile (0.25 miles) ?????

Anyway, Here is the method.

5.A) 1/4 mile = 0.25 mile

so,

distance = 65.5 - 0.25 = 65.25 miles

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5.B)  a = 55² / 2 * 0.25

a = 6050 miles / hr²

so,

t = v - u / a

t = 55 / 6050

t = 9.09e-3 hr

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5.C) t = 65.25 / 55

t = 1.186 hours

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5.D) 0.25 is x % of 65.5

so,

x = 0.38 %

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5.E) Total time = 1.19509 hours

so,

9.09e-3 is x % of 1.19509

x = 0.76 %