28. Distance-Time Graphs

1. Core Principles

• Function: Distance-time graphs allow us to visualize the distance an object travels over a specific period.

• The Gradient: The most important rule is that the gradient of the line represents the speed.

• This is because Gradient = Change in distance / Change in time

This is because , which is the formula for speed.

2. Interpreting the Shapes

• Straight Diagonal Line: Represents a constant speed. The steeper the line, the faster the object is moving.

• Horizontal (Flat) Line: Represents being stationary (speed is zero) because the distance is not changing as time passes.

• Curving Upwards: Indicates the gradient is getting steeper, meaning the object is accelerating.

• Curving Downwards: Indicates the gradient is leveling off, meaning the object is decelerating.

3. Calculating Speed

For Straight Lines

• Simply pick a section of the line and divide the distance traveled by the time taken.

• Example: If a cyclist travels 20 meters in 2 seconds, the speed is $20 / 2 = 10 \text{ m/s}$.

For Curves (Instantaneous Speed)

• If the speed is changing, you cannot use the whole section. Instead, you must find the speed at a specific point.

• Step 1: Draw a tangent to the curve at that specific point. A tangent is a straight line that touches the curve and has the same gradient as the curve at that point.

• Step 2: Calculate the gradient of that tangent by picking two points on it and dividing the change in distance by the change in time.

4. Summary Table