One-Dimensional Kinematics

Derive the set of kinematic equations for constant acceleration from first principles using calculus.

Apply constant acceleration equations to solve multi-stage motion problems, including vertical free-fall.

Solve problems with time-dependent acceleration, a(t), using direct integration.

Solve problems with velocity-dependent acceleration, a(v), using the method of separation of variables.

Solve problems with position-dependent acceleration, a(x), using the chain rule identity a = v(dv/dx).

Apply dimensional analysis and limiting case checks to verify solutions to complex 1D kinematics problems.