Question

A force of F = `("x"/2 + 15) "N"` acts on a particle. If x 2 is in metre, calculate the work done by the force during the displacement of the particle from x = 0 to x = 4 m

Options

• 128 J

• 80 J

• 64 J

• 52 J

Answer 1

64 J

Explanation:

W = `\int_("X"=0) ^("x"= 4)` F dx = `\int_("X"=0) ^("x"= 4) ("x"/2 +15)` dx

= `\int_("X"=0) ^("x"= 4)  "x"/2`  dx +  `\int_("X"=0) ^("x"= 4)` 15 dx

`= 1/2 ["x"^2 /2] _("x" = 0)^("x" = 4)+ 15  ["x"] _(x=0)^(x=4)`

`= 1/2 [(4^2 - 0)/2] + 15[4-0]`