How Is Engine Power Related to Velocity and Resistive Force in Automobiles?

[mjdiaz89]

Homework Statement

The engine of an automobile requires 40 hp to maintain a constant speed of 78 km/h.

(a) What is the resistive force against the automobile?
correct check mark
1376.465N (correct)
(b) If the resistive force is proportional to the velocity, what must the engine power be to drive at constant speeds of 65 km/h?
wrong check mark
hp
(c) What must the engine power be to drive at constant speeds of 145 km/h under the same conditions?
wrong check mark
hp

Homework Equations

P=Fv = $$\frac{Fd}{s}$$

The Attempt at a Solution

Questions B and C: It seems I have two unknowns (Resistive force and engine power output). Any ideas?

 

[lavalamp]

Since you are assuming that resistive force is directly proportional to velocity, you know:
$$F \propto v$$
$$F = kv$$

Therefore:
$$P = Fv$$
$$P = kv^{2}$$

You now need to find the constant k, then you'll be all set.