00:01
For this problem, we will use kinetic energy, power, and some properties of a car to solve some problems about the car.
00:08
First, we need to find how many gallons it takes to accelerate the car from rest to 55 miles per hour.
00:17
To do this, first we need the kinetic energy required to speed up the car to this velocity.
00:23
Canetic energy is equal to one -half, the mass times the final velocity is square.
00:29
In this case, the final velocity is 55 miles.
00:32
Per hour, which is 25 meters per second.
00:38
And the mass of the car is 900 kilograms, which gives us a kinetic energy of one half times 900 times 25 squared, which is 281 ,250 joules.
01:00
Now we need to calculate how much energy a gallon of gasoline delivers to the wheels.
01:12
We have that one gallon of gasoline produced.
01:16
This is 1 .34 times 10 to the 8th joules of energy, but the car is only 15 % efficient, so we multiply this by 0 .15, which gives us 2 .01 times 10 to the 7th joules of energy that's delivered to the wheels by the gas.
01:35
Now to find the number of gallons for this acceleration, we simply divide the energy required to do it...