Question #b0468

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Answer 1 · 2017-03-30T08:33:05

The answer is #A +4J#

The work done is equal to the change in kinetic energy.

#W=F*d#

Here, we have

#W=int_2^1F(x)dx#

#=int_2^1(2-4x)dx#

#=[2x-4/2x^2]_2^1#

#=(2*1-2)-(4-8)#

#=0-4+8=4#

The work done is #=4J#

Answer 2 · 2017-03-30T08:43:33

See below

Only to add variety in the types of response this question attracts.

From Newton's 2nd Law:

#F = m ddot x implies color(red)(2 - 4x = m dot x (d dot x)/dx )#

We separate and solve the DE:

#int_2^1 \ 2 - 4x \ dx = m int_(v_1)^(v_2) \ dot x \ d dot x #

# [ 2x - 2x^2 ]\_2^1 = 1/2 m ( v_2^2 - v_1^2) color(blue)(= Delta T) #

#implies Delta T = 4 J#