The amount of energy a car expends against air resistance is approximately given by
`E = K ADv^(2)`
where E is measured in Joules. K is a constant, A is the cross-sectional area of the car viewed from the front (in `m^(2)` ), D is the distance traveled (in m), and v is the speed of the car (in m/s). Julie wants to drive from Mumbai to Delhi and get good fuel mileage. For the following questions, assume that the energy loss is due solely to air resistance.
(a) Julie usually drives at a speed of 54 Km/hr. How much more energy will she use if she drives 20% faster ?
(b) Harshit drives a very large SUV car, and Julie drives a small car. Every linear dimension of Harshit's car is double that of Julie's car. Find the ratio of energy spent by Harshit's car to Julie's car when they cover same distance. Speed of Harshit was 10% faster compared to Julie's car.
(c) Write the dimensional formula for K. Will you believe that K depends on density of air?

Answer

(a) 44 % higher
(b) 4.84
(c) `[ML^(-3)]`; Yes