Kinematic equations, motion graphs, and free fall

When an object's acceleration is constant, four kinematic equations connect its displacement (d), starting velocity (v_i), final velocity (v_f), acceleration (a), and time (t): v_f = v_i + a t; d = v_i t + (1/2) a t^2; v_f^2 = v_i^2 + 2 a d; and d = (v_i + v_f) / 2 x t. The key step is choosing the equation that leaves out the one quantity you neither know nor need. Motion graphs show the same relationships: the slope of a position-time graph is velocity, the slope of a velocity-time graph is acceleration, and the area under a velocity-time graph is displacement. Free fall is motion under gravity alone, ignoring air resistance. Near Earth's surface, every freely falling object, heavy or light, accelerates downward at about 9.8 m/s^2, a value called g. A ball dropped from rest falls about 4.9 m in the first second and about 19.6 m in two seconds. A ball thrown straight up slows by 9.8 m/s every second, stops for an instant at the top, then speeds up on the way down. In real air, drag makes light, spread-out objects like feathers fall more slowly, and a falling object can reach a terminal velocity, where air resistance balances its weight and it stops speeding up.

This explanation is AI-generated and can occasionally be wrong. 🚩 Report