MATH 32A Lecture Notes - Lecture 8: Vector Projection
Document Summary
To understand acceleration, first we start with velocity: since t = v / ||v||, v = Remember, all of these are functions, not constant, functions of t. To get acceleration, take the derivative of velocity. A = dv/dt = d/dt(||v||t) = d||v||/dt (t) + ||v||t". Since n = t" / ||t"||, t" = ||t"|| n. Since k = ||t"|| / ||v||, ||t"|| = ||v|| k. T" = ||t"|| n = ||v|| k n. So, d||v||/dt (t) + ||v||t" = d||v||/dt t + ||v|| ||v|| kn = d||v||/dt t + k||v|| 2 n. d||v||/dt might not be zero. Yes, it"s a scalar (number), but it is changing over time. Imagine d||v||/dt as the function that defines ||v||. So, accleration is a scalar multiple of t plus a scalar multiple of n (k is a scalar). Review: projection of vector u to vector w = u || , line that goes from tip of u to.
