How Do You Calculate Kinetic and Potential Energy in Free Fall?

AI Thread Summary
To calculate kinetic and potential energy in free fall, one can use the formulas K = 1/2mv² and U = mgy, substituting the given functions for velocity v(t) and position y(t). The mass is 2 kg, and gravity is 10 m/s², with y(t) = 9 - 5t² and v(t) = -10t. The user initially struggled with expressing energy as a function of time but received guidance on correcting their approach. After clarification on the potential energy formula, the user successfully solved the problem. This discussion highlights the importance of correctly substituting variables in energy equations.
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Homework Statement



A mass m = 2 is in free fall. The acceleration of gravity is g = 10. All numbers are in mks units. The position y(t) and velocity v(t) of the mass as a function of time t are y(t)=9−5t2 and v(t)=−10t. Find each of the energies (K,U,E) as a function of time t. Hint: substitute v(t) into K(v), substitute y(t) into U(y).

Homework Equations



k = 1/2mv2
u = mgy

The Attempt at a Solution



I know that:
Work = ΔK
-ΔU = ΔK

im having trouble switching the equation to a function of time.
Am i trying to approach the problem in the wrong way?

any help is appreciated. Thanks!
 
Last edited:
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Your formula for ##U## is a little off. (Hint: check your units!)
 
oh okay i solved the problem thank you!
 
Sure thing, happy to help!
 

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