Types of acceleration

• Take the direction of the velocity as the positive direction.
• A small ball rolling on a smooth surface with different slopes shows all three cases:

1. Positive acceleration (velocity increases): e.g. the ball rolling down an inclined plane.
2. Zero acceleration (velocity constant): e.g. the ball rolling on a smooth horizontal surface. The change in velocity is zero.
3. Negative acceleration (velocity decreases — often called deceleration or retardation): e.g. the ball rolling up an inclined plane.

General rule about signs (very important):

• If velocity and acceleration have the same direction (same sign), the object speeds up — even if both are negative.
• If they have opposite directions (opposite signs), the object slows down.
• If acceleration = 0, the velocity is constant. It is not necessarily zero (e.g. a car at a steady 20 m/s has zero acceleration).

Life application.

• Inside every car there are three controls that change the velocity: the accelerator (gas) pedal increases the magnitude, the brake pedal decreases it, and the steering wheel changes its direction.
• Each of them produces an acceleration.