= Speed, Velocity, and Acceleration = '''Speed''', '''velocity''', and '''acceleration''' seem to be everyone's favorite example for teaching calculus. <> ---- == Definitions == For two given positions, there is a vector r⃗ between them. Taking the [[Calculus/Distance|distance]] of r⃗, i.e. ''||r⃗||'', gives the... distance. In ''R^1^'', velocity is the rate of change in position; speed would then be an equivalent concept. However, in higher dimensions velocity is a vector (e.g., ''v⃗ = dr⃗/dt = [dx/dt dy/dt dz/dt]'' in ''R^3^'') and speed is given by ''||v⃗||''. Acceleration is the rate of change in velocity. In higher dimension where velocity is a vector, so too is acceleration. For example, ''a⃗ = dv⃗/dt = [d^2^x/dt^2^ d^2^y/dt^2^ d^2^z/dt^2^]''. ---- CategoryRicottone