A force F = (cx - 3.00x^2)i^ acts on a virus as the virus moves along an x axis, with F measured in Newtons, x in meters, and c a constant. At x = 0, the virus’s kinetic energy is 20.0 J, while at x = 3.00 m, it is 11.0 J. Find c.

c = 4

Explanation:

From work-energy theorem KE = workdone.

Given F = (cx - 3.00x²)i

W = ∫Fdx = ∫(cx - 3.00x²)dx = cx²/2 –3.00x³/3 + A

W = cx²/2 –x³ + A

Where A is a constant

At x = 0, KE = 20J

So W = 20J at x = 0

20 = c×0 - 0 +A

A = 20

So W = cx²/2 –x³ + 20

Also when x = 3.00m, W = KE = 11J

So

11 = c×3²/2 – 3³ + 20

11 = 4.5c – 7

4.5c = 11 + 7

4.5c = 18

c = 18/4.5 = 4

c = 4

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