1. The problem statement, all variables and given/known data With a function that gives Force with respect to Displacement (F(x) = 2000-100x), is there a way to find a general formula for the time it takes from displacement 0 to 20? The force is acting on an object, pushing it horizontally. Assume no friction and no air resistance. 2. Relevant equations Force with respect to Displacement (x): F(x) = 2000-100x At 0 displacement, there's 2000 Newton of force acting on the object, and the force linearly decreases until there's no force at 20 meters away and beyond. 3. The attempt at a solution Work = ∫ from 0 to b of (F * dx) = ∫ from 0 to b of (2000-100x) dx = -50(b- 40)b Work = Final Kinetic Energy - Initial Kinetic Energy. Initially, the object is stationary with no initial velocity, so I'm assuming that the initial Kinetic Energy is 0. Work(b) = Kinetic Energy(b) = -50(b - 40)b = 0.5mv^2. Solving for v, I get: v(b) = sqrt((2/m) * -50(b - 40)b) From here, I'm tempted to plug velocity into this formula (Displacement = Velocity * Time) and solve for time, but I feel like this won't work.