The Physics of Constant Motion
When a vehicle moves at a constant velocity, it implies that its acceleration is zero. According to Newton's Second Law of Motion ($F_{net} = ma$), if $a = 0$, the net force acting on the object must also be zero.
In our scenario, the car is moving forward while experiencing a resistive frictional force. To maintain a constant speed, the engine must exert a forward force that exactly cancels out the frictional force.
The Problem
Given:
- Mass of the car ($m$) = $1000 \text{ kg}$
- Velocity ($v$) = $20 \text{ m/s}$
- Frictional Force ($f$) = $200 \text{ N}$
Goal: Find the power ($P$) developed by the engine.
Step-by-Step Solution
Determine the required engine force ($F$): Since the car moves at a constant speed, the driving force must be equal in magnitude to the frictional force. $F_{drive} = f = 200 \text{ N}$
Apply the Power Formula: Power is defined as the rate at which work is done. For a constant force acting in the direction of motion, power can be calculated as: $P = F \times v$
Calculate the result: $P = 200 \text{ N} \times 20 \text{ m/s}$ $P = 4000 \text{ Watts (or 4 kW)}$
Key Intuition
Many students mistakenly try to include the mass ($1000 \text{ kg}$) in the power calculation. However, if the speed is constant, the mass is only relevant if we were calculating the work needed to change its state or if there were gravitational potential energy changes involved. Here, the engine's job is simply to fight the friction continuously.