One-dimensional motion: v(t) = -(t+1) * sin(t^2 / 2)
how often does a particle following that function change direction in the open interval (0,3).
3 answers
It's part of an FRQ. I've been working at it for a while, but I have not gotten a single definitive answer.
I'm allowed to graph it using a graphing calculator, but I want to understand why it's once.
the particle changes direction when it stops and reverses. That is, when v(t) = 0
sin(t^2/2) = 0 when t^2/2 = kπ
That is, when t = √2π, √4π, ...
Only √2π is in the interval (0,3)
sin(t^2/2) = 0 when t^2/2 = kπ
That is, when t = √2π, √4π, ...
Only √2π is in the interval (0,3)
2 answers