Hello! I'm trying to model a car slowing down from speed with the forces of drag and friction and gravity from the road slope.. The model, which models the resistive forces is as follows.. [ Ffriction + Fdrag + Fslope ] / m = -a (deceleration) where: Friction force Ffriction = A where A = mg x Rd, m is mass, g is gravity Rd is the friction coefficient Drag force Fdrag = B v2 where B = 0.5 x ρ x A x Cd, ρ is density, A is frontal area, Cd is drag coefficient Force due to slope Fslope = C sin(θs) where C = mg, θs is the angle of the road at displacement s The displacement data is given in a discrete form.. for example, θ0 = 2.2° θ1 = 4.1° θ2 = 3.2° ... θn = x My ultimate goal is to have an equation that gives me displacement as a function of time.. given the parameters A, B, the initial velocity vi and the road angle information.. I've had success in modeling the car without accounting for the slope by solving the following differential equation (from the model..) -a = A + B v2 -s''(t) = A + B s'(t)2 Simply solving for s(t) (with wolfram alhpa..) I get an expression for displacement as a function of time and the coefficients A & B as well as constants on integration C1 & C2.. My question is.. how can I incorporate the road angle information? It would be easier the road angle information could be provided as a function of time, θ(t) instead of θ(s).. but both should be workable.. Thanks!