Car Braking Times and Variations
IB Mathematics SL
Research Report- Specimen Paper A
Given the stimulus word, Life, I started thinking of ways that I can use calculus in looking at vehicular dilemmas. I decided to see how long and how far it takes cars to stop. Approximately 1.3 million people die in road crashes each year, on average 3,287 deaths per day in the entire world. Within the first week of getting my first car I was rear-ended twice. Both situations could have easily been avoided by proper braking. This made me wonder how long it takes peoples cars to stop before a collision occurs. We all know that there are many factors that contribute to this such as rain, wear and tear on tires or brake pads, and human error. These variables
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The measure of velocity is distance divided by time. We also need to establish that the term “vehicle” in our case means a sedan or light truck. We also need to know the relationship between mph and fps. Mph =miles per hour, fps = feet per second. We use mph mutiplied by (1.467)=fps. Now we need to see what an average stopping time is. Over all cars, an average stopping ratio is about 15 fps. This is used when the street surface is dry and the vehicle has good tires (little wear). For example, if the initial velocity is 60 mph (88 fps), and the car is decelerating at an average of 15 fps, after 1 second the velocity would have been reduced to 73 fps. This would keep decreasing until the vehicle comes to a complete stop after about 6.87 seconds (this includes an extra second for delayed reaction time of the driver). This is calculated by (initial velocity)/ 15fps +1, so (88)/15+1=6.87seconds. Now that we have our stopping time we can find the distance it takes for a vehicle to stop. This is determined by the formula of ½ the initial velocity (in fps) multiplied by the time required to stop. In this case it works out to be ½(88)(6.87)= 302.28 feet. Remember, fps = …show more content…
86.53
40 58.7 144.21
50 73.4 216.29
60 88 302.28
70 102.7 402.93
To find the rate that a car decelerates we will use a deceleration function. This is just the opposite of the acceleration function. In this situation we are working with feet and seconds. The corresponding units for velocity (speed) will be feet per second (f/s) and for acceleration f/s2. The acceleration is in the opposite direction to the motion, and so the acceleration is negative. The following formula only relates the magnitudes of the distance travelled, initial velocity and acceleration.
The simple formula for the stopping distance is: d=u^2/2a • u is the initial velocity
• v is the final velocity
• a is the stopping distance of a car
• t is the time of motion
• d is the deceleration To find the rate of deceleration of the car at a given speed we can use the equation above. Let’s use our example from before of 60 mph. Remember that 60 mph is 88 fps. For this situation the measured stopping distance is 302.28 feet and the velocity at which the brakes are applied is 88
Stopping, just as important as acceleration the ability to slow or stop quickly and safely are important traits of performance, this can be indicated by braking distance from a certain speed, where a shorter stopping distance is more desirable measure of performance. The Corvettes performance shows that it fits the great sports car mold. Speed, power and the ability to hug the road, are all part of the experience of driving a truly great sports car. The Corvette delivers in all these areas, it has a 0-60 MPH time of less than 5 seconds, and a time of slightly less than 14 seconds in the quarter mile. In the 525 foot slalom test an average speed of 47.9 mph was obtained. On the skid pad the Corvette is able to obtain 0.96 lateral g’s (Stewart, 2007). The Corvette’s stopping power is noted in its ability to come to a complete stop from 60 miles per hour in only 125 feet (Mueller, 1998). These performance measures may not be used in everyday driving, but the ability to stop quickly in an emergency situation is apparent, as is having enough acceleration to merge onto a busy highway, with the performance the Corvette has, these everyday tasks can be accomplished effortlessly and safely.
1885 going at a top speed of 11 kilometers per hour. Now crossing the finish line as the first car in the world. Now 131 years later there are cars going 434 kilometers per hour. How did this happen? How does it affect people every day?
The word “fast” is used with different meanings. The car’s speed is what will be
The Walkers’ suits say the vehicle was travelling between 63 and 71 mph. After Walker’s death, his two brothers helped complete action scenes in Furious 7, which earned more than $1.5 billion globally when it was released in April.I thought this might interest you. Another Carrera GT bites the dust as a body shop mechanic who claimed he was going less than 30MPH smashed into a telephone pole. porsche said in November that Walker’s death was his own comparative fault.
As the car go down it looses its potential energy because it is not at the same height anymore. As it loses the potential energy it gains kinetic energy. Kinetic energy came along because of its high speed. The mathematical equation for this is initial kinetic energy plus initial potential energy plus external work equals final kinetic energy plus final potential energy. To find work the equation is force times distance. To find power the equation is work divided by time.
If a car is going 60 miles per hour, how far will it go in feet in 1 minute?
Next, the independent variable was the sail car and shed car. The speed acceleration was the dependent variable. The constants marble distance of photogate the angel of the track.
15) A cart starts from rest and accelerates at 4.0 m/s2 for 5.0 s, then maintain that velocity for 10 s, and then decelerates at the rate of 2.0 m/s2 for 4.0 s. What is the final speed of the car?
It is always important to keep in mind the requirements of the vehicle you are driving. If you have a larger vehicle, you may want to begin slowing down quicker than you would if you were driving a small car. This is because your vehicle has more mass and more energy is required to stop it. However, if you are driving a small vehicle, you may want to slow down a bit later than you would if you were driving a smaller vehicle so it has enough momentum to make the
If we measured in meters then a=4.9.) t is the time in seconds, v0 is the initial velocity of 30 feet per second, and s0 is the initial height or 4 feet. Thus we have:
When people learn to drive sometimes it is hard to try and stop in time. Most people can do it but others have a tough time when they are not paying attention to what is going on around them. Braking distance is traveled before coming to a complete stop.
Problem Statement: Some people were wondering what the velocity of a car launched down a ramp is and where it would land. The purpose of this is to compare the predicted values and experimental values found during the lab. Prediction: To find the velocity of the car and the distance in the x-direction it traveled; formulas must first be derived to find each unknown quantity. To find velocity, energy concept equations were used.
Acceleration and Speed are obviously the two defining characteristics of a fast car. Newton’s three laws of motion are an essential part in determining how fast a
The first is how far the car travels when the driver is reacting and braking (Transport for NSW, n.d.). As the speed of the car increases, the distance travelled between seeing an obstruction and pressing the brakes does too. The car’s inertia means that an increased speed requires a greater distance to brake to a complete stop. These mean that a car might still be travelling at high speeds upon impact (NSW Centre for Road Safety, 2016). Figure 1 shows the relationship between speed and distance travelled when reacting and braking. The second concept influenced, is the amount of kinetic energy that has to be absorbed upon impact (Transport for NSW, n.d.). To calculate kinetic energy the equation KE = ½mv2 is used (The Physics Classroom, n.d.). Looking at this, the fact that the value for speed is squared shows how significant speed is on the resulting kinetic
to review what they can and cannot do. In normal braking, a vehicle slows as its wheels are