When you’re driving, the distance it takes to stop your car in an emergency isn’t just about hitting the brakes. It’s a combination of two key factors: your reaction distance and your braking distance. Understanding these helps us see why distracted driving can be so dangerous.
Reaction distance is how far your car travels from the moment you see a hazard (like a sudden obstacle) to the moment you actually start applying the brakes. Even a short delay in reacting can make a big difference in the total stopping distance. Think about it: if you’re distracted, your reaction time will be longer, and your car will travel further before you even begin to slow down.
Braking distance is the distance your car travels from the moment you start braking until the car comes to a complete stop. This distance is affected by things like your speed, the condition of your brakes and tires, and the road surface.
Review the two short video clips below. The first shows a driver reacting to the appearance of an obstacle, applying the brakes, and coming to a stop. The second shows the same scenario, except that the driver was temporarily distracted—temporarily paying attention to something other than driving.
In your notebook, copy the table below and decide what events we should measure to best describe the motion of the car responding to the obstacle.
| Position | Math Symbol | Description |
|---|---|---|
| Position 0 | $x_0$ | |
| Position 1 | $x_1$ | |
| Position 2 | $x_2$ | |
| Position 3 | $x_3$ |
To really understand how reaction time and braking distance work, we can analyze the position of a car mathematically. By marking the car’s position at different points in time, we can visualize and calculate the distances traveled during the reaction and braking phases.
Revisit the videos above, but this time record measurements of the car’s distance travelled (from the origin) at each important position.
- Tape a strip of paper horizontally (landscape) across the width of your screen such that the car is visible above the paper.
- Run the video, pausing at important events and marking on the paper the location of the car at each important position.
- Label each mark with the mathematical symbol determined above ($x_0$, etc.)
Be sure to also record the position of the obstacle before removing your paper from the screen
Considerations
- How will you measure the position of the car? Front bumper? Perfect center? Front tire? Some other way?
- How can you tell when the driver begins braking? How will you determine when the car has come to a complete stop?
- Copy the table below into your science notebook
We can use a scale (like the known length of the car) to convert measurements from the video or a diagram into real-world distances. In these videos, the real-world length of the car was 4.5 m.
| Variable measured: | Measured on Screen (in m) |
Actual Value (in m) |
|---|---|---|
| Length of car | 4.5 | |
| Pre-obstacle distance ($ΔX_1$) | ||
| Reaction distance ($ΔX_2$) | ||
| Braking distance ($ΔX_3$) |
Instructions
- Using a ruler, determine the relative size (length) of the car in the videos. Record this value in your table (in m).
- Use a ruler to determine the lengths of the position intervals (distances from $x_0$ to each position). Record these values in the table above.
- Find the ratio of the actual length of the car (4.5 meters) to the length you measured. Set this ratio equal to the ratio of the actual distance of each position interval to the measured length of that interval. This relationship is illustrated in this equation:
\(\frac{\text{actual car length}}{\text{measured car length}} = \frac{\text{actual distance}\,(\Delta X)}{\text{measured} \,(\Delta X)}\)
- Solve to get the actual distances of each position interval and record each in the table above.
- Repeat your data collection for the distracted driver. Either use a new strip of paper or write on the back of the first, but be sure to indicate which is which.
- Calculate the reaction and braking distances for the distracted driver.
All change occurs over time, and understanding an object’s position in space requires knowing its position in time. Motion is inherently tied to the passage of time, as an object’s location can only be described relative to specific moments. This connection between space and time is fundamental to analyzing and predicting motion in all of physics.
- Use two new strips of paper to reconstruct a timeline of each driver stopping.
- Determine and record the time at which each important position was reached. Label each point with a corresponding position (example: the car was at position $x_0$ at the time $t_0$)
Table 1. Position and time data for a non-distracted driver reacting to an obstacle.
| Position | Time (s) | Distance (m) |
|---|---|---|
| $x_0$ | 0 | |
| $x_1$ | ||
| $x_2$ | ||
| $x_3$ |
A powerful way to visualize motion is by creating a position-time (P-T) graph. This type of graph plots the position of an object on the vertical axis (y-axis) against time on the horizontal axis (x-axis).
The table above contains position and time data that should look familiar from your mathematics classes. Each row represents a coordinate point (time, position) that can be plotted on an x-y coordinate system, with time on the x-axis and position on the y-axis. By plotting these points and connecting them, we create a mathematical model of the car’s motion that allows us to analyze patterns and calculate important values like velocity.
- Produce an x-y axis in your science notebook. One quadrant is sufficient as we have no negative values.
- Plot each point (time, position) on the coordinate axes. Use a ruler to ensure precision.
- Connect each plotted point with a straight line.
The slope of a position-time graph tells us about the object’s velocity (speed and direction).
From math class, the equation for slope should be familiar:
\[\text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in position}}{\text{change in time}} = \frac{\Delta x*}{\Delta t}\]$\text{*}$ note that in this example $\Delta x$ is on the vertical axis, even though $x$ is usually the horizontal axis, we are using the letter $x$ to represent position.
A student determined that the distance between $x_0$ and $x_1$ was 6.9 meters and the car took 1.9 seconds to travel that distance. The calculation for the car’s velocity would be:
\[slope = \frac{\Delta x}{\Delta t} = \frac{6.9\, meters}{1.9\,seconds} \approx 3.6\, \frac{m}{s}\]
- In a different color or line type or on a different graph entirely, produce a P-T graph of the distracted driver’s motion.
By comparing the position-time graphs for a non-distracted driver and a distracted driver, we can see how the longer reaction time of the distracted driver affects the overall motion and stopping distance. The graph for the distracted driver will show the car covering more distance at a constant speed during the reaction time before the slope changes due to braking.
Being distracted significantly increases your reaction time. This longer reaction time means your car travels a greater distance before you even begin to brake. While the braking process itself might be the same once the brakes are applied, the extra distance covered during the reaction time adds to the total stopping distance. This increased stopping distance can be the crucial difference between avoiding a collision and being involved in one.
Understanding the physics behind reaction time, braking distance, and how to analyze motion helps us appreciate the importance of staying focused while driving.