Final answer:
The drag force on a car increases by a factor of approximately 3.0 when the speed goes from 65 km/h to 110 km/h, as drag force is proportional to the square of velocity. Therefore, the correct option is d).
Step-by-step explanation:
The subject in question relates to the physics of drag force on an object moving through a fluid, which for a car is air resistance. The drag force experienced by a car is proportional to the square of its velocity, according to the drag equation:
Fd = ½ ρ Cd A v2
Where Fd is the drag force, ρ (rho) is the air density, Cd is the drag coefficient, A is the cross-sectional area, and v is the velocity of the car. When the car's speed changes from 65 km/h to 110 km/h, we are interested in the factor by which the drag force increases, which can be calculated by taking the ratio of the squares of these speeds.
Firstly, convert the speeds from km/h to m/s to be consistent with the standard SI units:
• 65 km/h = 18.06 m/s
• 110 km/h = 30.56 m/s
Then, calculate the factor increase in the drag force:
Factor = (30.56 m/s)2 / (18.06 m/s)2
Factor = (935.91 m2/s2) / (326.16 m2/s2)
Factor = 2.87
This calculation shows that the drag force increases by approximately factor of 2.87, which means the answer is (d) Increases by approximately 3.0 times.