Speed, velocity, and acceleration are all related to displacement over time, but they have different meanings and mathematical relationships:
Displacement: Displacement refers to the change in position or the distance and direction between the starting point and the ending point of an object's motion. It is a vector quantity, meaning it has both magnitude and direction.
Speed: Speed is a scalar quantity that represents the rate at which an object covers distance. It is the magnitude of the velocity vector and does not take into account the direction of motion. Speed is calculated by dividing the total distance traveled by the time taken, regardless of the direction of motion. Mathematically, speed = total distance / time.
Velocity: Velocity is a vector quantity that describes the rate at which an object changes its displacement. It takes into account both the magnitude and direction of motion. Velocity is calculated by dividing the change in displacement (Δx) by the change in time (Δt). Mathematically, velocity = displacement / time.
Acceleration: Acceleration is a vector quantity that represents the rate at which an object changes its velocity. It is the rate of change of velocity with respect to time. Acceleration can be positive or negative, indicating speeding up or slowing down, respectively. Acceleration is calculated by dividing the change in velocity (Δv) by the change in time (Δt). Mathematically, acceleration = change in velocity / time.
In summary, displacement is the change in position, speed is the rate of covering distance, velocity is the rate of change of displacement, and acceleration is the rate of change of velocity. Displacement and velocity are both vector quantities, while speed and acceleration are scalar quantities.