Force and Motion

Motion has three linked descriptions: where something is (position), how fast that position changes (velocity), and how fast velocity itself changes (acceleration). On a position-time graph, the slope at any instant is the velocity. On a velocity-time graph, the slope is the acceleration, and the area under the curve is the distance travelled. A flat velocity graph means zero acceleration, even if the object is moving fast. A straight-line velocity graph with a steady slope means constant acceleration, which shows up as a curved position graph.

A free-body diagram strips an object down to arrows: one for every force acting on it, drawn from its center, pointing in the direction each force pushes or pulls. Gravity points down, a normal force points away from the surface, friction points opposite the motion, an applied push or pull points wherever it's aimed. Add the arrows as vectors, cancel opposite ones, and what's left is the net force. That net force is what goes into Newton's second law: acceleration equals net force divided by mass, or F = ma.

This is also where inertia explains everyday motion that looks like magic. A body in motion stays in motion at constant velocity unless a net force acts on it. A passenger on a braking bus keeps moving forward because nothing is pulling them backward with the bus; their body simply continues at its old speed while the floor beneath them slows. The same law connects back to the graphs: no net force means a flat velocity line, and any push or pull bends that line into a slope.