Velocity

Definition

Velocity is the speed of an object and its direction of motion. While speed is a scalar quantity (magnitude only), velocity is a vector quantity (magnitude and direction).

Why It Matters

Speed tells you how fast you’re going; velocity tells you if you’re actually hitting the target. In both physics and business, high speed with the wrong velocity is just a faster way to reach the wrong destination.

Core Concepts

Relative Motion: All motion is relative. Motion is measured relative to a frame of reference (usually Earth).
Acceleration: The rate at which velocity changes with time. This can be a change in speed, direction, or both.
- $\text{Acceleration} = \frac{\Delta v}{\Delta t}$
- How to read: “Acceleration equals delta v over delta t.”
- Meaning: Change in velocity per unit time; average acceleration over interval $\Delta t$ .
Free Fall: An object falling under the influence of gravity alone. On Earth, the acceleration of free fall is $g \approx 10 \text{ m/s}^2$ $g \approx 10 m/s^{2}$ .
- How to read: “g approximately equals ten meters per second squared.”
- Meaning: Near-Earth gravitational acceleration; velocity increases by ~10 m/s each second.
  - Velocity in Free Fall: $v = gt$ $v = g t$ (starting from rest).
    - How to read: “v equals g times t.”
    - Meaning: Linear speed buildup from rest under constant $g$ .
  - Distance in Free Fall: $d = \frac{1}{2}gt^2$ $d = \frac{1}{2} g t^{2}$ .
    - How to read: “d equals one-half g t-squared.”
    - Meaning: Quadratic distance growth; displacement from rest under constant acceleration.
Average vs. Instantaneous:
- Average Speed = $\frac{\text{Total Distance}}{\text{Time Interval}}$ $\frac{Total Distance}{Time Interval}$
  - How to read: “Average speed equals total distance over time interval.”
  - Meaning: Scalar average; ignores direction changes.
- Instantaneous Speed = Speed at any specific moment.

Definition

Why It Matters

Core Concepts

Connected Concepts

Connected notes