Answer:
The speed of the particle at x = 4.0 m is 13.66 m/s
Explanation:
The work done by this force between the two points above is given by
W = ∫ F dx
W = ∫⁴₋₄ (-5x² + 7x) dx
W = [(-5x³/3) + (7x²/2)]⁴₋₄
W = [(-5(4³)/3) + (7(4²)/2)] - [(-5(-4)³)/3) + (7((-4)²)/2)] = (-50.6667) - (162.6667) = (- 213.33 J)
Kinetic energy at -4.0 m
At this point, v = 20 m/s
K.E = mv²/2 = 2 × 20²/2 = 400 J
To obtain the kinetic energy at 4 m,
We apply the work-energy theorem which mathematically translates to
The work done in moving a particle from one point to another = Change in kinetic energy of the particle between those two points
W = ΔK.E
Work done between x = - 4m and x = 4 m is - 213.33 J
Hence, ΔK.E = -213.33 J
Change in kinetic energy of the particle between x = - 4m and x = 4m is ΔK.E
ΔK.E = (Kinetic energy at x = 4m) - (kinetic energy at x = - 4m)
- 213.33 J = (mv²/2) - 400
mv²/2 = -213.33 + 400 = 186.67 J
2v² = 2 × 186.67
v² = 186.67
v = 13.66 m/s.
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