The apple in my hand has three different forms of energy that I can think of.
1). Thermal energy. I know that the apple's temperature is not absolute zero, because it is not freezing my hand off. Therefore it holds some heat energy.
2). Chemical energy. From previous experience, I know that if I eat the apple, it gives me a boost and keeps the doctor away, since my body is able to metabolize it, and extract nutrition from its chemical energy.
3). Potential energy. Also from previous experience, I realize that when I picked up the apple, I exerted force on it opposite to the force of gravity. By doing work on it, I endowed it with increased gravitational potential energy, which would immediately be obvious if I dropped it to the ground, where it would either smash or dig a little crater in the grass.
An object's acceleration is the rate its velocity (speed and direction) changes. Therefore, an object can accelerate even if its speed is constant - if its direction changes. If an object's velocity is constant, however, its acceleration will be zero.