How do you interpret the slope of a distance-time graph?

The slope of a distance-time graph represents the speed of the object.

In a distance-time graph, the distance travelled by an object is plotted on the vertical (y) axis, while the time taken is plotted on the horizontal (x) axis. The slope, or gradient, of the line on this graph indicates how quickly the distance changes with respect to time. Essentially, it tells you the speed at which the object is moving. A steeper slope means a higher speed, while a gentler slope indicates a lower speed.

To calculate the slope, you need to find the change in distance (Δy) divided by the change in time (Δx). This is often written as the formula: slope = Δy / Δx. For example, if an object travels 100 metres in 20 seconds, the slope of the line would be 100 metres / 20 seconds = 5 metres per second. This means the object is moving at a speed of 5 metres per second.

If the line on the graph is horizontal, the slope is zero, indicating that the object is stationary and not moving at all. Conversely, if the line is vertical, which is practically impossible in real-life scenarios, it would suggest an infinite speed, meaning the object would cover an infinite distance in zero time.

Understanding the slope of a distance-time graph is crucial for analysing motion. It helps you determine not just how far an object has travelled, but also how fast it was moving at any given point in time. This concept is fundamental in physics and is widely applicable in various real-world situations, from calculating the speed of a car to understanding the motion of celestial bodies.