Back to Splitting the Acceleration Vector

Activity 10.7.3

Avg difficulty 2.5

Compute the splitting of the acceleration for the curve given by r⃗(t)=⟨t,t22,t36⟩\vr(t)= \langle t, \frac{t^2}{2},\frac{t^3}{6} \rangle at t=1t=1. You should calculate aT⃗a_{\vT}, aN⃗a_{\vN}, T⃗\vT, and N⃗\vN. Additionally, you should verify a⃗=aT⃗T⃗+aN⃗N⃗\va = a_{\vT} \vT +a_{\vN} \vN and that T⃗\vT is orthogonal to N⃗\vN.

Long, Keller & Schlicker, Active Calculus Multivariable, §10.7 Splitting the Acceleration Vector, Activity 10.7.3

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Adapted from Active Calculus Multivariable © 2013–2026 Nicholas Long, Mitchel T. Keller, and Steven Schlicker. Licensed under CC BY-SA 4.0. Source: Active Calculus Multivariable. Imported at revision 692c03c.