Work by Variable Force — Prelims Questions

A particle moves along the x-axis from $x=0$ to $x=5,\text{m}$ under the influence of a force given by $F = (7 - 2x + 3x^2),\text{N}$. Calculate the work done by the force.

A force $vec{F} = (3x^2hat{i} + 4yhat{j}),\text{N}$ acts on a particle. Calculate the work done by this force as the particle moves from the origin $(0,0)$ to a point $(2,3),\text{m}$ along a straight line path.

The force-displacement graph for a particle is shown below. What is the work done by the force in moving the particle from $x=0,\text{m}$ to $x=6,\text{m}$?

A spring has a spring constant $k = 200,\text{N/m}$. What is the work done to stretch the spring from an extension of $2,\text{cm}$ to $5,\text{cm}$?

Which of the following statements is TRUE regarding work done by a variable force?

A particle is subjected to a force $vec{F} = (6xhat{i} + 8yhat{j}),\text{N}$. What is the work done by this force when the particle moves from $(1,1),\text{m}$ to $(2,2),\text{m}$?