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Physics 12: The Effect Of Speed on Stopping Distance

A closer look at the physics behind braking in a vehicle

Armaan Rajwani

on 14 October 2015

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Transcript of Physics 12: The Effect Of Speed on Stopping Distance

Speed Vs Stopping Distance
As you most probably know, I have a keen interest in cars and the design/ technology behind them. For this assignment, I chose to create a project that was closely related to both automotive and physics, respectively.
Time and time again, you see speeding drivers on the road fail to brake soon enough, creating an accident. But why is it so difficult to judge distance correctly? The answer lies within the physics related to an object in motion.
The crucial formula used to help answer this question is as follows: Vf² = Vi² + 2ad
Since there's more than one variable involved in judging distance, a more specific question is: What is the relationship between speed (initial velocity) and stopping distance (d)?
To carry out this experiment, I was going to use my car and brake from various speeds. After some more thought, I deemed that using my Go-Kart as a test vehicle was a better option since it is more robust and easier to fix.
So, without further ado, let's find out!
After reviewing the formula, Vf² = Vi² + 2ad, I predict that increasing the speed (Vi) by a factor of 2, the stopping distance (d) will increase by a factor of 4. In other words, doubling the speed will quadruple the stopping distance
acceleration remains constant
reaction time is near zero (negligible)
Painter's Tape
Metric Tape Measure
Mobile Device
Notepad & Pencil
4.Set tire pressure to 13 p.s.i. (approximately 1 bar) for all 4 tires.

5.Set the Go-Kart up far enough away from the braking zone so that there will be enough room to accelerate to the desired speed, and level off at that speed.

6.Using the masking tape, tape the iPhone or other mobile device to the steering wheel, and calibrate it in that position. Open the application that will be used.

7.The experiment can now begin.
1.Select an appropriate location to carry out the experiment. A flat, level parking lot or quiet street will be ideal.

2.Place the 2 pylons about 2 metres apart from each other (leaving enough room for the go-kart to pass in between). These pylons indicate the beginning of the braking zone.

3.Next to one of the pylons, place the first strip of masking tape on the ground. This will be the first distance marker. Using the metre stick, place down the remaining strips of tape every 1 metre. 20 metres will be adequate.
1.Get the “all clear” from the helper.

2.Accelerate smoothly to the desired speed and then maintain that speed. Confirm with the steering wheel mounted device.

3.The instant the front bumper is in line with the pylons, apply the brakes as hard as possible. If the axle locks up and the wheels skid, do not count that run. The braking force must put the tires on the brink of lock-up, without quite making them do so. Lock-up will cause the tires to “flat-spot” and render them useless.

4.Once the Go-Kart comes to a full stop, calculate the braking distance using the masking tape strips as a reference.

5.To acquire more accurate data, it would be best to do 4 to 6 runs at each speed, and then take an average of these results. Record the braking distances in the table.
Photo of the complete setup
To ensure that there was only one variable throughout the testing, I calculated the maximum acceleration at each speed. The shortest stopping distance (marked "L" in the table) was used in the calculations.
10 km/h
Vf² = Vi² + 2ad
a = (Vf² - Vi²)/(2d)
a = (0-2.77²)/(2(0.75))
a = -5.14 m/s²
20 km/h
Vf² = Vi² + 2ad
a = (Vf² - Vi²)/(2d)
a = (0-5.55²)/(2(3.0))
a = -5.14 m/s²
30 km/h
Vf² = Vi² + 2ad
a = (Vf² - Vi²)/(2d)
a = (0-8.33²)/(2(6.75))
a = -5.14 m/s²
40 km/h
Vf² = Vi² + 2ad
a = (Vf² - Vi²)/(2d)
a = (0-11.11²)/(2(11.5))
a = -5.37 m/s²
50 km/h
Vf² = Vi² + 2ad
a = (Vf² - Vi²)/(2d)
a = (0-13.89²)/(2(18.5))
a = -5.21 m/s²
The experiment that I conducted helped confirm my hypothesis. The results showed that by doubling the initial velocity of an object, the distance it requires to stop (while subjected to the same acceleration) will increase four-fold.
Note: modulating brake pressure to allow maximum braking force, while avoiding lock up, proved to be quite tricky. Runs where the wheels locked up are denoted as "L/U" in the table. These were not used for shortest stop calculations.
I feel that I received such consistent results because I tested in similar conditions whenever possible. By keeping other parameters the same, it allowed me to narrow down the testing to a single variable, being Vi (speed). My results had a ±5% error AT MOST. This could have easily been caused by human error (incorrect pedal pressure, variation in reaction times), differences in friction between pads/disc and tires/road, respectively, among other things.
by Armaan Rajwani
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