Kinetic Energy problem i think

AI Thread Summary
Accelerating a car from 20-30 m/s requires more energy than from 10-20 m/s due to the greater change in kinetic energy. The kinetic energy formula, KE = 1/2mv^2, shows that energy increases with the square of the velocity. Calculations reveal that the change in kinetic energy for the first interval is 150 joules, while the second interval is 250 joules. Thus, the additional energy required to accelerate from 20-30 m/s is 100 joules. This confirms that higher speeds necessitate more energy for acceleration.
nlsed
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Homework Statement



What takes more energy? Accelerating a car from 10-20m/s or from 20-30m/s? Why?

Homework Equations





The Attempt at a Solution



Since KE = 1/2mv^2, I suppose the higher the velocity is the more kinetic energy the car will have, but I have no clue how to solve this problem.
 
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Won't the bigger change in kinetic energy require the greater energy?
You know that conservation of energy thing?

Plug in the numbers.
 
then change in kinetic energy equals the work done, which one requires more work?
 
so is this right? since m is constant it is just 1kg

1/2mv2
1/2(1kg)(10m/s)2 = 50 joules
1/2(1kg)(20m/s)2 = 200 joules
1/2(1kg)(30m/s)2 = 450 joules

KE for (10-20m/s) = 150 joules
KE for (20-30m/s) = 250 joules

So accelerating from 20-30m/s requires 100 more joules of energy?
 
Last edited:
nlsed said:
So accelerating from 20-30m/s requires 100 more joules of energy?

That should do it.
 
Thank you very much! :!)
 
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