(Solved): The given function represents the position of a particle traveling along a horizontal line. \[ s(t) ...

The given function represents the position of a particle traveling along a horizontal line. \[ s(t)=\frac{t}{1+t^{2}} \text { for } t \geq 0 \] (a) Find the velocity and acceleration functions. \( v(t)=\frac{t^{3}+t^{2}-t+1}{\left(1+t^{2}\right)^{2}}{ }_{x} \) \( a(t)=\frac{3 t^{2}+2 t}{2(1+t)(1)} \prod_{X} \) (b) Determine the time intervals when the object is slowing down or speeding up. (Enter your answers using interval notation.) slowing down speeding up