An object of mass 500 g, initially at rest, is acted upon by a variable force whose X-component varies with X in the manner shown. The velocities of the object at the points X = 8 m and X = 12 m, would have the respective values of (nearly)
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From work-energy theorem we know that
K = work = area under F - x graph
From x = 0 to x = 8 m
mv 2 = 100 + 30 2
v 2 = 520
From x = 0to x=12m
mv 2 =100 + 30-47.5 + 20
Hence appropriate option is 23 m/s and 20.6 m/s
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