A particle moves along the $y$-axis with velocity given by $v ( t ) = t \sin \left( t ^ { 2 } \right)$ for $t \geq 0$. (a) In which direction (up or down) is the particle moving at time $t = 1.5$ ? Why? (b) Find the acceleration of the particle at time $t = 1.5$. Is the velocity of the particle increasing at $t = 1.5$ ? Why or why not? (c) Given that $y ( t )$ is the position of the particle at time $t$ and that $y ( 0 ) = 3$, find $y ( 2 )$. (d) Find the total distance traveled by the particle from $t = 0$ to $t = 2$.
A particle moves along the $y$-axis with velocity given by $v ( t ) = t \sin \left( t ^ { 2 } \right)$ for $t \geq 0$.\\
(a) In which direction (up or down) is the particle moving at time $t = 1.5$ ? Why?\\
(b) Find the acceleration of the particle at time $t = 1.5$. Is the velocity of the particle increasing at $t = 1.5$ ? Why or why not?\\
(c) Given that $y ( t )$ is the position of the particle at time $t$ and that $y ( 0 ) = 3$, find $y ( 2 )$.\\
(d) Find the total distance traveled by the particle from $t = 0$ to $t = 2$.