A force F = 3x2 + 2x + 1 acts on a body in the x -direction. The work done by this force during a displacement from x = -1 to +1 is

Question

A force F = 3x2 + 2x + 1 acts on a body in the x -direction. The work done by this force during a displacement from x = -1 to +1 is (A)  2 units (B)  4 units (C)  6 units (D)  8 units

Tardigrade Admin · Accepted Answer

F=3x2+2x+1 W=∫ limits-11Fdx =∫ limits-11 (3x2+2x+1)dx =[x3+x2+x]-11 ⇒ 3+1 4 units

Q. A force $F = 3 x^{2} + 2 x + 1$ acts on a body in the $x$ -direction. The work done by this force during a displacement from $x = - 1$ to $+ 1$ is

$2$ units

$4$ units

$6$ units

$8$ units

$F = 3 x^{2} + 2 x + 1$
$W = - 1 \int 1 F d x = - 1 \int 1 (3 x^{2} + 2 x + 1) d x$
$= [x^{3} + x^{2} + x]_{- 1}^{1}$
$\Rightarrow 3 + 1$
$4$ units

Q. A force F=3x2+2x+1 acts on a body in the x -direction. The work done by this force during a displacement from x=−1 to +1 is

2 units

4 units

6 units

8 units