Kinematics with calculus: position, velocity and acceleration are linked by derivatives and integrals, so motion with changing acceleration is fair game. This unit covers vectors in unit-vector notation, instantaneous rates, graphs, reference frames and motion in two dimensions, the language for every later unit in Physics C.
Scalars have magnitude only; vectors have magnitude and direction. Vectors can be written as a magnitude and direction or in unit-vector notation, A = Aₓî + A_yĵ + A_zk̂, and a resultant is found by adding components.
Displacement is change in position; average velocity and acceleration use the start and end states. As the interval shrinks to zero they become instantaneous: v = dx/dt and a = dv/dt. Differentiate to go from position to velocity to acceleration; integrate to go back.
Motion can be shown with diagrams, graphs, equations and words. For constant acceleration, three kinematic equations apply (g = 10 m/s² near Earth). Slopes of x–t and v–t graphs give v and a; areas under v–t and a–t graphs give Δx and Δv.
What an observer measures depends on their reference frame. Velocities convert between frames by vector addition; all inertial frames measure the same acceleration. Frames are inertial unless stated otherwise.
Motion in 2-D or 3-D splits into independent 1-D components that share time; velocity and acceleration can differ by direction and need not be uniform. A projectile has zero horizontal acceleration and constant vertical acceleration. 2-D motion is quantitative; 3-D is qualitative.