Could someone please help me determine the steps/process of working through this

Question

Could someone please help me determine the steps/process of working through this problem? I am confused as to how to correctly complete it.

Chapter 7
Reality Check – Gas Mileage on Short Trips
I notice when I drive my kids to school, about a 1 mile trip, my Toyota Sienna minivan gets horrible gas mileage (10- 15 mpg). I notice on the way to school, we need to stop 5 times. Each time we stop, we need to use gas to increase our kinetic energy. A Toyota Sienna minivan has a mass of 3000 kg. When starting from rest, we accelerate to 30 mph. In this problem, we will determine the gas mileage theoretically.
a.) How much Kinetic Energy does a the van have when it is traveling at 30 mph?
b.) One gallon of gas stores 1.38 x 108J of energy. Because of the efficiency of a gas engine, one gallon of gas can only produce 3.5 x 107 J of Kinetic Energy. Determine how much gasoline is needed to accelerate the car from 0 to 30 mph 5 times.
c.) At cruising, my van gets 25 mpg. If I drove the one mile to school without stopping, how much gas would be required.
d.) use your answers to b and c along with the 1 mile trip to school to estimate the gas mileage of my van on this trip.

Explanation / Answer

a)

v = speed = 30 mph = 13.41 m/s

m = mass = 3000 kg

kinetic energy is given as

KE = (0.5) m v2

KE = (0.5) (3000) (13.41)2

KE = 2.7 x 105 J

b)

Total KE = 5 ( 2.7 x 105 ) = 13.5 x 105 J

energy given by gas = 3.5 x 107 J/gallon

n = number of gallons = Total KE /energy given by gas = (13.5 x 105 )/(3.5 x 107) = 0.0386 gallon

c)

distance = 1 mile

mileage = 25 mpg

volume of gas = distance / mileage = 1/25 = 0.04 gallon

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