given the function vecrt43t t3vec12t2vec a find the tangential and normal components of the acce

Name: given the function vecrt43t t3vec12t2vec a find the tangential and normal components of the acceleration vector b when is the particle speeding up 81722
Uploaded: 2022-05-31T09:45:04-08:00
Duration: 5 min 1 s
Channel: Adi S
Description: given the function vecrt43t t3vec12t2vec a find the tangential and normal components of the acceleration vector b when is the particle speeding up 81722

Step 1: Find the velocity vector (vec{v}(t)) by differentiating the position vector (vec{r}

Question

Given the function vec(r)(t)=4(3t-t^(3))vec(ı)+(12t^(2))vec(ȷ). a. Find the tangential and normal components of the acceleration vector. b. When is the particle 'speeding up'?

          Given the function vec(r)(t)=4(3t-t^(3))vec(ı)+(12t^(2))vec(ȷ).
a. Find the tangential and normal components of the acceleration vector.
b. When is the particle 'speeding up'?

Added by Brian N.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

05/31/2022

Step 1

Given: \[ \vec{r}(t) = 4(3t - t^3)\vec{\imath} + (12t^2)\vec{\jmath} \] Differentiate \(\vec{r}(t)\) with respect to \(t\): \[ \vec{v}(t) = \frac{d}{dt} \left[ 4(3t - t^3)\vec{\imath} + (12t^2)\vec{\jmath} \right] \] \[ \vec{v}(t) = 4 \left[ 3 - 3t^2 \right] Show more…

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Given the function vec(r)(t)=4(3t-t^(3))vec(ı)+(12t^(2))vec(ȷ). a. Find the tangential and normal components of the acceleration vector. b. When is the particle 'speeding up'?