(a)

The particle speeds up when the velocity is positive and increasing

Thus, from the graph it happens in the interval and . 

The particle speeds down when the velocity is positive and decreasing.

Thus, from the graph it happens in the interval . 

(b)

The particle speeds up when the velocity is positive and increasing

There is no such interval in that kind.

and the particle also speeds up when the velocity is negative and decreasing

Thus, from the graph it happens in the interval . 

The particle speeds down when the velocity is positive and decreasing.

Thus, from the graph it happens in the interval .

and the particle also speeds down when the velocity is negative and increasing

Thus, from the graph it happens in the interval .

(a)

Speeding up when or

Slowing down when

(b)

Speeding up when or

Slowing down when or