When it comes to objects like cars or people, an increase in speed requires more energy due to the relationship between force, work, and energy.
The basic principle is that the work done on an object is equal to the force applied multiplied by the distance over which the force is applied. Mathematically, work (W) can be expressed as W = F × d, where F represents the force applied and d represents the distance.
When an object is in motion, its speed is related to the amount of work and energy required to sustain that speed. The energy needed to accelerate or maintain the speed of an object is proportional to the square of its velocity.
When an object increases its speed, the force required to maintain that speed also increases. According to Newton's second law of motion (F = ma), if the mass (m) remains constant, an increase in speed (velocity) results in a higher acceleration (a). This higher acceleration requires a greater force to counteract the resistive forces like friction and air resistance.
To provide this additional force, more energy is needed. In the case of a car, it requires a more powerful engine or motor to generate the force required to overcome the increased resistance and propel the vehicle at higher speeds. Similarly, in the context of a human running or cycling, an increase in speed requires greater muscular effort and energy expenditure to overcome air resistance and maintain the higher velocity.
Therefore, as speed increases, the force required to sustain that speed increases, leading to a greater energy demand.