Speed and Distance/Time Graphs

Turning Motion into Numbers

Once you know how to describe motion using a frame of reference, the next step is measuring it. Speed tells you how quickly an object's position is changing — specifically, how much distance it covers in a certain amount of time. If the truck in our crash scenario travels 60 meters in 3 seconds, its speed is 20 meters per second. That single number lets you compare the truck's motion to a bicycle, a sprinting cheetah, or another car, no matter how different those situations look.

Speed is calculated by dividing distance traveled by the time it took: speed = distance ÷ time. It sounds simple, but this one relationship is the foundation for predicting almost everything about how objects move, including how much time a driver has to react before hitting something.

Reading a Distance vs. Time Graph

Numbers are useful, but graphs let you see motion at a glance. A distance vs. time graph plots how far an object has traveled (on the vertical axis) against how much time has passed (on the horizontal axis). The steepness of the line — its slope — tells you the object's speed. A steep line means the object is covering a lot of distance in a short time, so it's moving fast. A flatter line means it's moving slowly, and a perfectly flat, horizontal line means the object has stopped completely.

If you saw a distance vs. time graph for our crash-test truck, you'd expect to see a fairly steep, straight line right up until the moment of impact — and then the line would go completely flat, because the truck's distance from its starting point stops increasing the instant it slams into the pole. That sudden change in slope, from steep to flat, is a graph's way of showing a sudden, dramatic stop.

Using Graphs to Predict a Crash

Here's why this matters beyond just reading charts: if you know an object's speed and its distance from an obstacle, you can predict when and how hard it will hit. Engineers and safety researchers actually do this kind of analysis using real recorded motion data. Tools like Vernier Graphical Analysis let scientists and students collect motion data from sensors — for example, tracking a toy car rolling toward a barrier — and instantly turn that data into a distance vs. time graph.

By studying the slope of that graph, you could estimate the truck's speed in the seconds before the crash and use it to predict how much force the impact would involve. This is exactly the kind of thinking real crash-safety engineers use to design safer cars, better seatbelts, and smarter warning systems.