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.

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.