A particle moves with position function $\mathbf { r } ( t ) = \left( 21 t - 7 t ^ { 3 } - 5 \right) \mathbf { i } + 21 t ^ { 2 } \mathbf { j }$.
Find the tangential component of the acceleration vector.
A) $a _ { T } = 5 t$
B) $a _ { T } = 542 t$
C) $a _ { T } = 42 t + 5$
D) $a _ { T } = - 55 t$
E) $a _ { T } = 42 t$

Question

Quizplus · Accepted Answer

The tangential component of acceleration is the derivative of the speed. First, find the velocity $\mathbf{v}(t)$ by differentiating $\mathbf{r}(t)$, then find the speed $|\mathbf{v}(t)|$, and differentiate it to get $a_T$. The correct answer is $a_T = 42t$.

A Particle Moves with Position Function r(t)=(21t−7t3−5)i+21t2j\mathbf { r } ( t ) = \left( 21 t - 7 t ^ { 3 } - 5 \right) \mathbf { i } + 21 t ^ { 2 } \mathbf { j }r(t)=(21t−7t3−5)i+21t2j

A Particle Moves with Position Function $\mathbf { r } ( t ) = \left( 21 t - 7 t ^ { 3 } - 5 \right) \mathbf { i } + 21 t ^ { 2 } \mathbf { j }$