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Question

question in picture

Answer 1

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Work-Energy Theorem says that the work of the force changes the kinetic energy of the mass. 

FΔx = ΔKThe constant force is F = (Kf - K₀) / (xf - x₀) = (0 - 24) / (5.0 - 0) = -4.8 N

When x is -3.1 m

ΔK = FΔx

(K - 0) = -4.8(-3.1 - 5.0)

K = 38.88 J

at which time the velocity is

33.88 = ½(7.0)v²

v = ± 3.33295...

We choose the negative vector value to fit the narrative, but the request is for speed so the absolute value .

When rounded to the two significant digits of the question numerals

v = 3.3 m/s

Answer 2

When the object passes back through x = 0, its KE will again be 24J.  The dK/dx will continue to be (24J)/(-5m) as x goes from 0 to -3.1 m.  When x = -1, you'll have K = 48J; when x = -2, you'll have K = 72J; when x = -3, you'll have K = 96J; when x = -3.1 m you'll have K = 98.4 J.