Let the position function of a particle be $\mathbf { r } ( t ) = \left\langle t ^ { 2 } , 2 t , e ^ { t } \right\rangle$ . Find the velocity of the particle when t = 1.
A) $( 2,2,1 )$

B) $( 2,2 , e )$
C) $(2,0,1 )$
D) $( 2,0 , e )$
E) $( 1,1,1 )$
F) $( 1,1 , e )$

G) $( 1,0,1 )$

H) $( 1,0 , e )$

Question

Let the position function of a particle be $\mathbf { r } ( t ) = \left\langle t ^ { 2 } , 2 t , e ^ { t } \right\rangle$ . Find the velocity of the particle when t = 1.
A) $( 2,2,1 )$

B) $( 2,2 , e )$
C) $(2,0,1 )$  
D) $( 2,0 , e )$ 
E) $( 1,1,1 )$ 
F) $( 1,1 , e )$

G) $( 1,0,1 )$

H) $( 1,0 , e )$

Quizplus · Accepted Answer

The velocity of the particle is given by the derivative of the position function $\mathbf{r}(t)$ with respect to time $t$, which is $\mathbf{v}(t) = \frac{d}{dt}\mathbf{r}(t) = \left\langle 2t, 2, e^t \right\rangle$. Substituting $t = 1$ gives $\mathbf{v}(1) = \left\langle 2(1), 2, e^1 \right\rangle = (2, 2, e)$.

Let the Position Function of a Particle Be r(t)=⟨t2,2t,et⟩\mathbf { r } ( t ) = \left\langle t ^ { 2 } , 2 t , e ^ { t } \right\rangler(t)=⟨t2,2t,et⟩

Let the Position Function of a Particle Be $\mathbf { r } ( t ) = \left\langle t ^ { 2 } , 2 t , e ^ { t } \right\rangle$