1. Speed vs. Velocity:

* Speed: How fast an object is moving, without regard to its direction. It's a scalar quantity (magnitude only).

* Velocity: How fast an object is moving *and* in what direction. It's a vector quantity (magnitude and direction).

2. Acceleration:

* Acceleration: The rate at which an object's *velocity* changes over time. It's a vector quantity.

* Key point: Acceleration is about *changes in velocity*, not just changes in speed. This means an object can accelerate even if its speed remains constant if its direction changes.

Examples:

* Constant Speed, No Acceleration: A car driving at a steady 60 mph on a straight road has constant speed but zero acceleration.

* Changing Speed, Acceleration: A car speeding up from 0 to 60 mph has acceleration.

* Changing Direction, Acceleration: A car driving around a curve at a constant speed still accelerates because its direction is changing.

How they work together:

* Positive Acceleration: Means the velocity is increasing (speeding up or changing direction in a way that increases velocity).

* Negative Acceleration (Deceleration): Means the velocity is decreasing (slowing down or changing direction in a way that decreases velocity).

Formula:

The relationship between acceleration, velocity, and time is captured in the following formula:

* Acceleration (a) = (Change in Velocity (Δv)) / (Change in Time (Δt))

In summary:

Acceleration is the key to understanding how an object's motion changes. It tells us how the velocity (speed and direction) of an object is changing over time.