A position-dependent force F=3 x2-2 x+7 acts on a body of mass 7 kg and displaces it from x=0 m to x=5 m. 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

A position-dependent force F=3 x2-2 x+7 acts on a body of mass 7 kg and displaces it from x=0 m to x=5 m. The work done on the body is x' joule. If both F and x are measured in SI units, the value of x' is (A) 135 (B) 235 (C) 335 (D) 935

Tardigrade Admin · Accepted Answer

This is the case of work done by a variable force W=∫ limits05(3 x2-2 x+7) d x W=|x3+x2+7 x|05 or W=(5 × 5 × 5-5 × 5+7 × 5) Or W=(125-25+35)=135 J

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

135

235

335

935

This is the case of work done by a variable force
$W = 0 \int 5 (3 x^{2} - 2 x + 7) d x$
$W = ∣ ∣ x^{3} + x^{2} + 7 x ∣ ∣_{0}^{5}$
or $W = (5 \times 5 \times 5 - 5 \times 5 + 7 \times 5)$
Or $W = (125 - 25 + 35) = 135 J$

Q. A position-dependent force F=3x2−2x+7 acts on a body of mass 7kg and displaces it from x=0m 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

135

235

335

935

This is the case of work done by a variable force W=0∫5​(3x2−2x+7)dx W=∣∣​x3+x2+7x∣∣​05​ or W=(5×5×5−5×5+7×5) Or W=(125−25+35)=135J

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

This is the case of work done by a variable force
$W = 0 \int 5 (3 x^{2} - 2 x + 7) d x$
$W = ∣ ∣ x^{3} + x^{2} + 7 x ∣ ∣_{0}^{5}$
or $W = (5 \times 5 \times 5 - 5 \times 5 + 7 \times 5)$
Or $W = (125 - 25 + 35) = 135 J$