Cars accelerating
An older model car accelerates from 0 to speed b in 10 seconds. A newer, more powerful sports car accelerates from 0 to 2v in the same time. What is the ratio of the powers expended by the two cars?
Shouldn't it just be twice the power since it reached twice the velocity?
Answer
You should be very careful here because you need a clearer understanding of the relationship between velocity and Power.
With velocity you know how much energy was used. In this case you would be considering kinetic energy (T). Additionally, power is simply the amount of energy used for a specific amount of time. Since total energy is T in this case then you simply consider that n times a certain energy is also n times the original power. On top of the being true, T α v^2.
With this information you should know how to solve the problem.
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You should be very careful here because you need a clearer understanding of the relationship between velocity and Power.
With velocity you know how much energy was used. In this case you would be considering kinetic energy (T). Additionally, power is simply the amount of energy used for a specific amount of time. Since total energy is T in this case then you simply consider that n times a certain energy is also n times the original power. On top of the being true, T α v^2.
With this information you should know how to solve the problem.