Calculus 3 (MA 113),Quiz 7, NAME:
° °
dT
dT °
dT °
°). To show T(t)⊥ dT ,
(5 pts) 1. Show that T(t)⊥
(Note that this shows T⊥N since N =
/°
°
dt
dt
dt °
dt
2
remember to start with kT(t)k = 1 =⇒ kT(t)k = 1 =⇒ T(t) · T(t) = 1 and then differentiate.
° °
° °
° °
° dT °
° and derive κ = ° dT ° / kvk .
(5 pts) 2. Start with the definition of curvature, i.e. κ = °
° dt °
° ds °
d
(kvk) T+ kvk2 κ N by starting
dt
v
,rewriting as v = kvk T, and differentiating (you will eventually need to use
with T = kvk
the result in (2)).
(5 pts) 3. Derive the decomposition of acceleration formula a =