Unit 4 - Problem 4 ==>Maximum car speed

How fast given horsepower and air resistance?

• Resistance in joules is: $$R_{air} = b*v^2 = .1{V^2}$$
• Power consumed is: $$P_{resistance} = R * V$$
• Because:  $$F_{resistance} \frac{D}{t} = \frac{(F_{resistance}*D)}{t} = \frac{W}{t} = P$$
• Car has 150 hp where 1 hp = 746 watts
• Power of the car in watts: $$W_{car} = 150 * 746 = 111,900$$
• Top speed is when power of resistance equals the power of the car: $$.1{V^3} = 150 * 746$$
• $$V^3 = 1,119,000$$
• In meters/second: $$V_{max} = 103.8$$