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17 February, 08:09

A particle moves along the plane curve C described by r (t) = ti+t2j. Find the curvature of the plane curve at t=2. Round your answer to two decimal places.

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  1. 17 February, 10:51
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    The curvature of the plan curve at t=2 is 0.

    Step-by-step explanation:

    First, we find take a derivative of r (t) = ti + t^2j

    r' (t) = i + 2tj

    we can also write it like r' (t) =

    Now, we take a magnitude of it

    |r' (t) | = √ (1) ^2 + (2t) ^2

    |r' (t) | = √17

    Now, we assume a variable T (t)

    T (t) = r' (t) / |r' (t) |

    T (t) = (i + 2tj) / √17

    T (t) = 1/√17 ()

    Take derivative of T (t)

    T' (t) = 1/√17 ()

    |T' (t) | = √ (1/√17) ^2 + (0) ^2 + (2) ^2

    |T' (t) | = √69/17

    Therefore,

    Curvature = |T' (t) | / |r' (t) |

    Curvature = (√69/17) / √17

    Curvature = √69.
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