A position-dependent force $F = 3x^{2} - 2x + 7$ acts on a body of mass 7 kg and displaces it from $x = 0$ m to $x = 5m$. The work done on the body is $x'$ joule. If both $F$ and $x$ are measured in SI units, the value of $x'$ is

Question

Dr. Abubacker · Accepted Answer

(a) This is the case of work done by a variable force
$W = \int_{0}^{5}{(3x^{2} - 2x + 7)dx}$
$W = \left| x^{3} + x^{2} + 7x ight|_{0}^{5}$
or $W = (5 	imes 5 	imes 5 - 5 	imes 5 + 7 	imes 5)$
or $W = (125 - 25 + 35) = 135\ J$

Q. A position-dependent force $F = 3x^{2} - 2x + 7$ acts on a body of mass 7 kg and displaces it from $x = 0$ m to $x = 5m$. The work done on the body is $x'$ joule. If both $F$ and $x$ are measured in SI units, the value of $x'$ is

Explanation

Reviewed by Dr. Abubacker

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