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The paths r(t)=(12, t3)" (t) = (t", t") and r1(t)=(t4, t6)"1 (t) = (e", t") trace the same curve, and r1(1)=r(1)."1 (1) = r (1). Do you expect either the velocity vectors or the 10. acceleration vectors of these paths at t=lt = 1 to point in the same direction? Explain. Compute these vectors and draw them on a single plot of the curve.

The paths r(t)=(12, t3)" (t) = (t", t") and r1(t)=(t4, t6)"1 (t) = (e", t") trace the same curve, and r1(1)=r(1)."1 (1) = r (1). Do you expect either the velocity vectors or the 10. acceleration vectors of these paths at t=lt = 1 to point in the same direction? Explain. Compute these vectors and draw them on a single plot of the curve.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The paths r(t)=(t2, t3)* (t) = (t², t*) and r1(t)=(t4, t6)*1 (t) = (t", t) trace the same curve, and r1(1)=r(1)."1 (1) = r (1). Do you expect either the velocity vectors or the %3D 10. acceleration vectors of these paths at t=lt = 1 to point in the same direction? Explain. Compute these vectors and draw them on a single plot of the curve.
Transcribed Image Text:The paths r(t)=(t2, t3)* (t) = (t², t*) and r1(t)=(t4, t6)*1 (t) = (t", t) trace the same curve, and r1(1)=r(1)."1 (1) = r (1). Do you expect either the velocity vectors or the %3D 10. acceleration vectors of these paths at t=lt = 1 to point in the same direction? Explain. Compute these vectors and draw them on a single plot of the curve.
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