Multivariable Calculus + Calc III - Motion Along a Curve

10 28 22
LECTURE 29
e recall the velocity wrt t is vet r t
V t is the instantaneous rate of changeof arc
length wrt
therefore dat is called the speed of theparticle
t
IT t
speed is also the magnitude of t that is Il ret 11
If the position of a particle wrt t is ret
and s is an arc length parameter then
act IES Th Kit Edt Nct
basically means that a t lies in the plane
of T t and N t and is always orthogonal to Bet
Prove the above theorem
t of TH we know T H IIT t 11 N t
t d t If T t
t If th If I T t 11 Nlt

Since we K f IIT t I
know u r t and Ilr't till daf
t If Tht t dat Kit Nlt In
tangential formaldirection direction
alt is always orthogonal to B t and lies in
the plane of Nlt and Tht
notation at If an K t
a t at f TCHTANGINCH
If a particle ha position of ret then
at each time t the vectors r a and
scalars K at an are related by
at YE an lived
a v11 YjProve the above theorem
a at TH t an N t
art att T t an N T At Http at
at a T
we know T Fry so
at Of A

2 an YEH
ax t att x T t an NXT Ot Blt Blt
me Blt r t x r t
know 11 r t x r t 11 1
axt Iffy an H Nlt
Ft KUNCH
an
FI an Et kit
an 11 9,11 a an II V11 Kit
s K Mitt YES in