A driver notices that her 950-kg car, when in neutral, slows down from 95 km/h to 65 km/h in about 7.0 s on a flat horizontal road. Approximately what power (watts and hp) is needed to keep the car traveling at a constant 80 km/h?

검증된 단계별 안내

Convert all given speeds from km/h to m/s. Use the conversion factor: 1 km/h = 1000 m / 3600 s. For example, \( v = 95 \text{ km/h} \) becomes \( v = \frac{95 \times 1000}{3600} \text{ m/s} \). Perform similar conversions for 65 km/h and 80 km/h.

Calculate the deceleration (negative acceleration) of the car while it slows down. Use the kinematic equation \( a = \frac{v_f - v_i}{t} \), where \( v_f \) is the final velocity, \( v_i \) is the initial velocity, and \( t \) is the time interval.

Determine the resistive force acting on the car due to friction and air resistance. Use Newton's second law: \( F = ma \), where \( m \) is the mass of the car and \( a \) is the deceleration calculated in the previous step.

Calculate the power required to overcome this resistive force and maintain a constant speed of 80 km/h. Use the formula for power: \( P = Fv \), where \( F \) is the resistive force and \( v \) is the constant velocity (in m/s).

Convert the power from watts to horsepower (hp) using the conversion factor: \( 1 \text{ hp} = 746 \text{ W} \).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion, calculated using the formula KE = 1/2 mv², where m is mass and v is velocity. In this scenario, understanding the kinetic energy of the car at different speeds is crucial for determining the energy required to maintain a constant speed against resistive forces.

Power

Power is the rate at which work is done or energy is transferred, expressed in watts (W) in the SI system. It can be calculated using the formula P = W/t, where W is work done and t is time. In this context, calculating the power needed to maintain a constant speed involves understanding the work done against forces like friction and air resistance.

Forces Acting on the Car

When a car is in motion, various forces act upon it, including gravitational force, friction, and air resistance. To maintain a constant speed, the power output must counteract these forces. Analyzing these forces helps in determining the net force required to keep the car moving at 80 km/h, which is essential for calculating the necessary power.