PHYS 1A Lecture Notes - Lecture 3: Classical Mechanics, Derivative
Document Summary
Displacement: how far you are from where you started. Speed is the change in distance travelled over a given time period. Velocity is the change in displacement after a given time period. Average- change in position over a finite time interval. Instantaneous: displacement during an infinitesimal time interval v(t) = lim(t->0) (change in x)/(change in time = dx/dt. First derivative of a function describes slope week 1 page 1. They have the same velocity where the slope is the same. So, the velocities are not the same at time tb. They are the same velocity sometime before tb. The change of velocity with time - a vector quantity. Average- change in velocity over a finite time. a= v/t. Instantaneous - change in velocity over an infinitesimal time interval. (second derivate of dx/dt) First derivative describes the slope of its graph. So the derivative of a velocity graph is acceleration. Second derivative of a function describes its graphs curvature.
