Question

3. (40 pts.) A particle travels from ($-\frac{1}{3}$,1,-2) to (9,9,6). Its motion is described by the position function $\vec{r}(t) = \langle \frac{t^3}{3}, t^2, 2t\rangle$. a) Find the distance the particle travels along the path, its average speed, and its displacement [the distance it could have traveled if in a straight line]. b) List a detailed snapshot of the T,N,B frame for this particle at the halfway point (by time) including curvature and torsion.

          3. (40 pts.) A particle travels from ($-\frac{1}{3}$,1,-2) to (9,9,6). Its motion is described by the
position function \(\vec{r}(t) = \langle \frac{t^3}{3}, t^2, 2t\rangle\).
a) Find the distance the particle travels along the path, its average speed, and its
displacement [the distance it could have traveled if in a straight line].
b) List a detailed snapshot of the T,N,B frame for this particle at the halfway point (by
time) including curvature and torsion.

3. (40 pts.) A particle travels from (-(1)/(3),1,-2) to (9,9,6). Its motion is described by the
position function r⃗(t) = ⟨(t^3)/(3), t^2, 2t⟩.
a) Find the distance the particle travels along the path, its average speed, and its
displacement [the distance it could have traveled if in a straight line].
b) List a detailed snapshot of the T,N,B frame for this particle at the halfway point (by
time) including curvature and torsion.

Added by Wesley S.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

05/24/2023

Step 1

To find the time interval, we need to determine when the particle reaches its final position (9,9,6) using the position function vec(r)(t) = (t^3/3, t^2, 2t). We can set each component of the position function equal to the corresponding component of the final Show more…

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A particle travels from (-(1)/(3),1,-2) to (9,9,6). Its motion is described by the position function vec(r)(t)=(:(t^(3))/(3),t^(2),2t:) a) Find the distance the particle travels along the path, its average speed, and its displacement [the distance it could have traveled if in a straight line]. b) List a detailed snapshot of the T,N,B frame for this particle at the halfway point (by time) including curvature and torsion. 3.(40 pts.) A particle travels from (-,1, -2) to (9,9,6). Its motion is described by the position function rt)=t2,2t). a) Find the distance the particle travels along the path, its average speed, and its displacement [the distance it could have traveled if in a straight line]. b) List a detailed snapshot of the T,N,B frame for this particle at the halfway point (by time) including curvature and torsion.