A force of (5 + 3x) N acting on a body of mass 20 kg along the x - axis displaces it from x = 2 m to x = 6 m . The work done by the force is

Question

A force of (5 + 3x) N acting on a body of mass 20 kg along the x - axis displaces it from x = 2 m to x = 6 m . The work done by the force is (A) 20 J (B) 48 J (C) 68 J (D) 86 J

Tardigrade Admin · Accepted Answer

Force F=(5+3 x) N Work done W=∫ limitsx1x2 F ⋅ d x=∫ limits26(5+3 x) d x =[5 x+(3 x2/2)]26=68 J

Q. A force of $(5 + 3 x) N$ acting on a body of mass $20 k g$ along the $x$ - axis displaces it from $x = 2 m$ to $x = 6 m$ . The work done by the force is

20 J

48 J

68 J

86 J

Force $F = (5 + 3 x) N$
Work done $W = x_{1} \int x_{2} F \cdot d x = 2 \int 6 (5 + 3 x) d x$
$= [5 x + \frac{3 x ^{2}}{2}]_{2}^{6} = 68 J$

Q. A force of (5+3x)N acting on a body of mass 20kg along the x - axis displaces it from x=2m to x=6m . The work done by the force is