I read the following on howstuffworks.com, and their explanation just doesn't seem correct to me.(adsbygoogle = window.adsbygoogle || []).push({});

"One of the interesting things about kinetic energy is that it increases with the velocity squared. This means that if a car is going twice as fast, it has four times the energy. You may have noticed that your car accelerates much faster from 0 mph to 20 mph than it does from 40 mph to 60 mph. Let's compare how much kinetic energy is required at each of these speeds. At first glance, you might say that in each case, the car is increasing its speed by 20 mph, and so the energy required for each increase must be the same. But this is not so.

We can calculate the kinetic energy required to go from 0 mph to 20 mph by calculating the KE at 20 mph and then subtracting the KE at 0 mph from that number. In this case, it would be 1/2*m*20^2 - 1/2*m*0^2. Because the second part of the equation is 0, the KE = 1/2*m*20^2, or 200 m. For the car going from 40 mph to 60 mph, the KE = 1/2*m*602 - 1/2*m*40^2; so KE = 1,800 m - 800 m, or 1000 m. Comparing the two results, we can see that it takes a KE of 1,000 m to go from 40 mph to 60 mph, whereas it only takes 200 m to go from 0 mph to 20 mph. "

The way they explain this implies that it is more difficult for an object that is already in motion to accelerate further. Wouldn't this imply that a greater force is necessary to accelerate an object at higher speeds than at lower speeds? As far as I can remember F=ma and neither acceleration nor force is affected by current velocity (excluding velocities that are near the speed of light, of course).

Also, doesn't kinetic energy depend on frame of reference as well? If you are already moving at 20 mph as in the example at a constant speed, couldn't your frame of reference just as easily be 0 mph? I realize that with the way a car's engine works and the way it is geared, air resistance, friction, etc, this may not be true, but what about if it was a space ship in a perfect vacuum? It doesn't seem that if you had two identical rockets used for thrust that the first rocket used would accelerate you more or more quickly than the second rocket used does just because your velocity relative to earth was now higher after firing off the first rocket.

Thank you for your explanations.

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# Question about energy requirements for acceleration

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