Force, Velocity, and Power

1. Mar 21, 2008

mjdiaz89

1. The problem statement, all variables and given/known data
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

2. Relevant equations
P=Fv = $$\frac{Fd}{s}$$

3. The attempt at a solution
Questions B and C: It seems I have two unknowns (Resistive force and engine power output). Any ideas?

2. Mar 21, 2008

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.