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: $$ V_{max} = 103.8 $$