Kinetic Energy problem i think

[nlsed]

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.

 

[LowlyPion]

Won't the bigger change in kinetic energy require the greater energy?
You know that conservation of energy thing?

Plug in the numbers.

 

[lubuntu]

then change in kinetic energy equals the work done, which one requires more work?

 

[nlsed]

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?

 

[LowlyPion]

So accelerating from 20-30m/s requires 100 more joules of energy?

That should do it.

 

[nlsed]

Thank you very much! :!)