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The force applied against an object moving horizontally on a linear path is described by #F(x)= x+2 N #. By how much does the object's kinetic energy change as the object moves from # x in [ 1 , 3 ]#?

Answer 1

Emily Abbate

Chang in KE = work done against force=#int_1^3F(x)dx# #=int_1^3(x+2)dx=[x^2/2+2x]_1^3# #=3^2/2+2xx3-1^2/2-2xx1=8J#

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Answer 2

Axel Acevedo

To find the change in kinetic energy, you need to integrate the force function over the given interval and use the work-energy theorem. The change in kinetic energy is equal to the work done by the force. So, integrate the force function F(x) from x = 1 to x = 3 to find the work done, then use that to find the change in kinetic energy.

The integral of F(x) from 1 to 3 is ∫(1+2)dx from 1 to 3. This equals (x^2/2 + 2x) evaluated from 1 to 3, which is (9/2 + 6) - (1/2 + 2) = 13.

Therefore, the change in kinetic energy is 13 Joules.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.