Solving Force Problems: Work Done from x=0 to x=4m

[brad sue]

Hi, I try to solve the following problem but my answer does not correspond to the solution of the textbook. Please help me to understand the problem:
The net force acting on a particle depends on the position of the particle along the x-axis according the relation F=F₀+C*x, where F₀=5N and C=-2N/m. The particle is initially at rest at x=0m when the force begins to act.
a- Calculate the work done by the force when the particle reaches x values 1,2,3and 4 m?
b- Determineany positions ( besides x=0m ) where the work done is zero.

I have problem for the question a.
What I did is to compute F₁=F₀+C*(1) [for x=1m]
that gives me F₁=5-2=3N
So the work for F₁ is W₁= F₁*(1)=3J
However the answer in the textbook it 4J I don't know how they get that.
Thank you for your time.
B

 

[Diane_]

You're neglecting the fact that the force is not constant over any distance.

If you know calculus, you can do this by integrating the force over the distance.

If you don't, then consider: since the force changes linearly, you could calculate an average force over a given distance without loss of rigor.

One thing, whichever way you do it - note the negative on your constant. What does that mean physically?