Find the velocity of a particle with the given position function. $$\mathbf { r } ( t ) = 19 e ^ { 5 t } \mathbf { i } + 5 e ^ { - 21 t } \mathbf { j }$$
A) $\mathbf { v } ( t ) = 19 e ^ { 5 t } \mathbf { i } + e ^ { - 21 t } \mathbf { j }$
B) $\mathbf { v } ( t ) = 95 e ^ { 5 t } \mathbf { i } - 105 e ^ { - 21 t } \mathbf { j }$
C) $\mathbf { v } ( t ) = 19 e ^ { 5 t } \mathbf { i } - 105 e ^ { - 21 t } \mathbf { j }$
D) $\mathbf { v } ( t ) = e ^ { 5 t } \mathbf { i } + 105 e ^ { - 21 t } \mathbf { j }$
E) $\mathbf { v } ( t ) = 95 e ^ { 5 t } \mathbf { i } + 105 e ^ { - 21 t } \mathbf { j }$

Question

Quizplus · Accepted Answer

The velocity $\mathbf{v}(t)$ is the derivative of the position function $\mathbf{r}(t)$. Differentiating each component of $\mathbf{r}(t)$ with respect to $t$ gives $\mathbf{v}(t) = 95e^{5t}\mathbf{i} - 105e^{-21t}\mathbf{j}$.

Find the Velocity of a Particle with the Given Position r(t)=19e5ti+5e−21tj\mathbf { r } ( t ) = 19 e ^ { 5 t } \mathbf { i } + 5 e ^ { - 21 t } \mathbf { j }r(t)=19e5ti+5e−21tj

Find the Velocity of a Particle with the Given Position $\mathbf { r } ( t ) = 19 e ^ { 5 t } \mathbf { i } + 5 e ^ { - 21 t } \mathbf { j }$