Acceleration- Whether an object is speeding up, slowing down, or changing direction, it is accelerating. Most amusement park rides involve acceleration. On a downhill slope or a sharp curve, a ride will probably increase in velocity or accelerate. While moving uphill or in a straight line, it may decrease in velocity or decelerate. The force of gravity pulling a roller coaster down hill causes the roller coaster to go faster and faster, it is accelerating.
Speed- distance divided by time or the rate at which an object (the roller coaster) moves. Speed, velocity and acceleration are all-important concepts to understand when building a roller coaster.Roller coasters must balance between thrills and safety. The ride should be as safe as possible. On the other hand, passengers ride a coaster for the death-defying thrill. The key to a successful coaster is to give the rider the thrill of speed and acceleration. It all comes down to speed control. To achieve this, the hills, curves, dips, straight aways, braking systems and loops are not randomly designed. They are carefully designed by engineers who have a deep understanding of the science of motion, properties of materials and structural design and a keen understanding of safety
Velocity- Velocity differs from speed in that velocity tells not only the speed at which a roller coaster is moving but also its direction. If a roller coaster goes around a bend or a loop, even if its speed is not changing, its velocity is changing because its direction of motion is changing; this change requires the application of a force. Roller coasters trade height for velocity and velocity for height. Most all calculations rely on using velocity measurements in one way or another.