1. The problem statement, all variables and given/known data Let's say that a ramp is modelled using the equation y = cx2, where c is a constant. Assuming a motorcycle starts at speed vi, displacement xi=0 and launches off the ramp at a horizontal displacement of xf, what is the motorcyclists speed and direction? 2. Relevant equations y = cx2 gradient = m = tan(θ) F = gsin(θ) F = ma 3. The attempt at a solution The gradient at each point, x, is given by: dy/dx = m = 2cx For an inclined plane, m = tan(θ), so from above: tan(θ) = 2cx θ = tan-1(2cx) The force down the slope at any point is F = gsin(θ), so: F = gsin(tan-1(2cx)) = (2cxg)/√(1+4x2) a = F/m = (2cxg)/(m√(1+4x2)) V = ∫adt, but the acceleration is in terms of x so I'm not sure what to do... I obviously need to find a way to link the displacement to the velocity, but I'm not sure how.