Quadratic Spline InterpolationPart 1 of 2

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Quadratic Spline ExampleThe upward velocity of a rocket is given as a function of time. Using quadratic splines Find the velocity at t=16 seconds Find the acceleration at t=16 seconds Find the distance covered between t=11 and t=16 seconds

tv(t)sm/s0010227.0415362.7820517.3522.5602.9730901.67

Data and Plot

tv(t)sm/s0010227.0415362.7820517.3522.5602.9730901.67

SolutionLet us set up the equations

Each Spline Goes Through Two Consecutive Data Points

Each Spline Goes Through Two Consecutive Data Points

tv(t)sm/s0010227.0415362.7820517.3522.5602.9730901.67

Derivatives are Continuous at Interior Data Points

Derivatives are continuous at Interior Data PointsAt t=10At t=15At t=20At t=22.5

Last Equation

Final Set of Equations

Coefficients of Spline

iaibici1022.704020.88884.92888.883-0.135635.66-141.6141.6048-33.956554.5550.2088928.86-152.13

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Quadratic Spline InterpolationPart 2 of 2

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Final Solution

Velocity at a Particular Pointa) Velocity at t=16

Acceleration from Velocity Profileb) Acceleration at t=16

Acceleration from Velocity ProfileThe quadratic spline valid at t=16 is given by,

Distance from Velocity Profilec) Find the distance covered by the rocket from t=11s to t=16s.

Distance from Velocity Profile

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