Physics Concepts and Motion Graphs

Physics Concepts

### Speed vs. Velocity

Speed: A scalar quantity that refers to how fast an object is moving. It has only magnitude.
- Measured in meters per second (m/s) or kilometers per hour (km/h).

- Example: A car moving at $60$ km/h.

Velocity: A vector quantity that refers to the rate at which an object changes its position. It has both magnitude and direction.

• Measured in meters per second (m/s) with a direction (e.g., $30$ m/s North).
• Example: A car moving at $60$ km/h due North.

### Displacement

Definition: The straight-line change in position. It's a vector quantity.

• Measured in meters (m) or kilometers (km) with a direction.

- Formula: $\Delta x = x<em>f - x</em>i$, where $\Delta x$ is displacement, $x<em>f$ is the final position, and $x</em>i$ is the initial position.

Special Case: If an object returns to its starting point, its displacement is zero, even if the distance traveled is not.

• Example: A round trip results in zero displacement regardless of the distance covered.

### Acceleration

Definition: The rate of change of velocity over time. It's a vector quantity.

• Measured in meters per second squared (m/s²).

- Example: A car accelerating from rest to $20$ m/s in $5$ seconds.

Formula: $a = \frac{v<em>2 - v</em>1}{t}$

• Where:
  • $a$ is acceleration
  • $v_2$ is the final velocity
  • $v_1$ is the initial velocity
  • $t$ is the time interval

### Calculating Average Velocity

Formula:
Average velocity = $\frac{\text{Total displacement}}{\text{Total time}}$

• Example: If a car travels $100$ meters East in $10$ seconds, its average velocity is $10$ m/s East.

### SI Units

Speed: meters per second (m/s)

Acceleration: meters per second squared (m/s²)

Rearranging Acceleration Formula

• $v<em>2 = v</em>1 + at$
• $v<em>1 = v</em>2 - at$
• $t = \frac{v<em>2 - v</em>1}{a}$

Motion Graphs

Position-Time Graph

• The slope of a tangent line at any point on a position-time graph gives the instantaneous velocity at that point.
  • A steeper slope indicates a higher velocity.
  • A horizontal line indicates zero velocity (object is at rest).

Velocity-Time Graph

• The area under the velocity-time graph gives the displacement of the object.
  • An area above the x-axis indicates positive displacement.
  • An area below the x-axis indicates negative displacement.

Sample Physics Topics to Review

• Interpreting direction in velocity problems (N, S, left, right). The sign of the velocity (positive or negative) indicates direction relative