Work Kinetic energy using variable force

AI Thread Summary
The discussion revolves around calculating work done by a variable force on a 2 kg mass described by the position function x(t) = 4t^3 - 6t. The user successfully calculated the work done between t=1 and t=3 seconds as 10,368 J using the change in kinetic energy. For part (b), the user inquired about finding the object's velocity when the force is zero, leading to the conclusion that the acceleration is given by 24t. Ultimately, it was confirmed that the velocity at time t=0 is -6 m/s. The conversation emphasizes understanding the relationship between force, acceleration, and velocity in the context of kinetic energy.
kjamha
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Homework Statement


The position of an object of mass 2 kg is changing as a function of time by the formula x(t) = 4t^3-6t. (a) find the work done by the forces acting on the particle between t=1 and t=3s. (b) What is the object's velocity when the force on it is zero?

Homework Equations


is my work for part (a) correct?
I do not know how to approach b.

The Attempt at a Solution


I took the derivative of the equation
12(t)^2 - 6 at t=1s and t=3s
to find vi and vf (I have vi = 6 m/s and vf = 102 m/s).
Then I used W = change in KE
1/2 x 2(102^2) - 1/2 x 2 (6^2) = 10,368 J.
Is that correct?
I'm not sure how to start part b
 
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And the time derivative of velocity is?
 
Are you asking for the acceleration?
 
kjamha said:
Are you asking for the acceleration?
Yes. Acceleration. Does that help for part b?

Your answer to a) is correct.
 
kjamha said:

Homework Equations


is my work for part (a) correct?
I do not know how to approach b.

kjamha, your Relevant equations aren't equations. You should place equations that you think are relevant to the type of problem being solved in that portion of the template.
 
taking the derivative, I would get acceleration = 24t
if F = 0, then 0 = 24t and t would have to be 0
find the velocity at time 0
12(t)^2 - 6 = -6
is the answer -6 m/s?
 
gneill said:
kjamha, your Relevant equations aren't equations. You should place equations that you think are relevant to the type of problem being solved in that portion of the template.
ok - I read it quickly and thought it said relevant questions.
 
kjamha said:
taking the derivative, I would get acceleration = 24t
if F = 0, then 0 = 24t and t would have to be 0
find the velocity at time 0
12(t)^2 - 6 = -6
is the answer -6 m/s?
Yes, that's correct.
 
PeroK said:
Yes, that's correct.
Thank you!
 
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