What are three ways an object can accelerate?

Answer 1

First, the definition of acceleration: "A change in velocity". Next, recognize that velocity is a vector and thus has both magnitude and direction.

Here's my best guess of what they are looking for:

1. The simplest case is when an object is moving in a straight line and the speed is changing.
2. An object moving in a circle at a constant angular rate (and therefor a constant linear speed tangent to the circle of motion) has an acceleration because the direction is changing.
3. An object moving in a circle at an angular rate that is changing.