Note that all objects are either in motion or not, and that they either have Potential Energy (or energy that can be used when called upon (needed)) or Kinetic Energy (or energy that is being used currently).

In the event of a person speeding, the person is exerting enough force using the gas pedal, giving a higher Kinetic Energy. The faster they are going, the higher the amount of Kinetic. If the driver is not paying attention and is going extremely fast, they may hit another car (for example). That car, in this example, is stopped for a red light. Unless the mass of the object is significantly bigger by a large margin, the transfer of energy from the Kinetic Energy to the object (with potential energy) would be visible. When a car hits another car of similar tonnage and size, the Kinetic Energy from the moving object would overcome the Potential Energy, changing that into a Kinetic Energy, forcing the stationary object to move forward. If there is a line of cars, then it would create a chain effect, which would lead to "greater damage".

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