For time $t \geq 0$, a particle moves in the $x y$-plane with position $( x ( t ) , y ( t ) )$ and velocity vector $\left\langle ( t - 1 ) e ^ { t ^ { 2 } } , \sin \left( t ^ { 1.25 } \right) \right\rangle$. At time $t = 0$, the position of the particle is $( - 2,5 )$. (a) Find the speed of the particle at time $t = 1.2$. Find the acceleration vector of the particle at time $t = 1.2$. (b) Find the total distance traveled by the particle over the time interval $0 \leq t \leq 1.2$. (c) Find the coordinates of the point at which the particle is farthest to the left for $t \geq 0$. Explain why there is no point at which the particle is farthest to the right for $t \geq 0$.
For time $t \geq 0$, a particle moves in the $x y$-plane with position $( x ( t ) , y ( t ) )$ and velocity vector $\left\langle ( t - 1 ) e ^ { t ^ { 2 } } , \sin \left( t ^ { 1.25 } \right) \right\rangle$. At time $t = 0$, the position of the particle is $( - 2,5 )$.\\
(a) Find the speed of the particle at time $t = 1.2$. Find the acceleration vector of the particle at time $t = 1.2$.\\
(b) Find the total distance traveled by the particle over the time interval $0 \leq t \leq 1.2$.\\
(c) Find the coordinates of the point at which the particle is farthest to the left for $t \geq 0$. Explain why there is no point at which the particle is farthest to the right for $t \geq 0$.