The mass ratio of objects A and B is . Both objects start fr...

Question

The mass ratio of objects A and B is . Both objects start from rest and undergo uniform acceleration along a frictionless horizontal surface under the action of the same force. When the two objects have traveled the same distance, what is the ratio of their kinetic energies?

Since both objects experience the same constant force F, the acceleration of each object can be determined using Newton's Second Law F = ma:

For object A with mass , the acceleration is:

For object B with mass , the acceleration is:

To find the velocity of each object after traveling a certain displacement, we use the kinematic equation:

where is the velocity, is the acceleration, and is the distance traveled.

For object A after traveling a distance :

For object B after traveling a displacement :

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