Find the curvature K of the curve at the point P. r(t) = 3ti + 2t^2j, P

iohanetc

iohanetc

Answered question

2021-09-21

Find the curvature K of the curve at the point P.
r(t)=3ti+2t2j,P(3,2)

Answer & Explanation

casincal

casincal

Skilled2021-09-22Added 82 answers

r(t)=3ti+2t2j
Differentiate
r(t)=3i+4tj
Find magnitude
|r(t)|=9+16t2
P(-3,2) corresponds to t=-1 at that point.
We have
r(t)=9+16(1)2=5
DIfferentiate r(t). To get
r(t)=0i+4j
r(t)×r(t)=(3i+4tj)×4j
r(t)×r(t)=12k+0
|r(t)×r(t)|=12
Recall that:
Curvature =|r(t)×r(t)||r(t)|3
Hence the curvature is
1253=12125

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