Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

1. Most of the gasoline that is used to power a car is burned during acceleratio

ID: 1881159 • Letter: 1

Question

1. Most of the gasoline that is used to power a car is burned during acceleration. Answer the following questions related to this process, neglecting any drag or friction on the car, and assuming a car has a mass of 1000 kg (a little over 1 ton) How much energy is required for a car to accelerate from 0 to 100 km/h over a distance of 100 m in kJ? (5 pts) a. How much energy is required for a car to accelerate from 0 to 100 km/h on an incline of 30° over a distance of 100 m in kJ? (5 pts) b. c. The energy density of gasoline is ~50 MJ/kg. If the density of gasoline is 700 kg/m3, how many liters (L) of gasoline are burned in the above two cases (no incline AND incline of 30°)? (Hint: 1 m#1000 L) (5 pts)

Explanation / Answer

Given,

m = 1000 kg ;

a)u = 0 ; v = 100 km/h = 27.78 m/s ; d = 100 m

we know that

v^2 = u^2 + 2 a s

27.78^2 = 0^2 + 2 x a x 100

a = 27.78^2/200 = 3.86 m/s^2

F = ma = 1000 x 3.86 = 3860 N

E = F d = 3860 x 100 = 386,000 = 386 kJ

Hence, E = 386 kJ

b)till F it remains same

E = F d cos(theta)

E = 3860 x 100 x cos30 = 334,000 J

Hence, E = 334 kJ

c)E' = E/V = E rho/m

m = E rho/E'

for first case

m = 386 x 10^3 x 700/50 x 10^6 = 5.404 kg

m' = 334 x 10^3 x 700/50 x 10^6 = 4.68 kg

Hence, m = 5.404 kg ; m' = 4.68 kg