Transportation: Ch. 1, Act. 3 Stopping Your Car Transportation: Ch. 1, Act. 3

What you already know Response time: The time between seeing an event and being able to react to it. Speed: The change in distance over time. v = d/t

Effect of Speed on Reaction time Think about being in a large box with no windows set in a truck with super-smooth suspension riding on a perfect straight highway Can you tell how fast you are going? Would you expect your reaction time to change as your speed increased?

Effect of Speed on Reaction time As speed increases, does it take longer to react? No. What is the relationship between speed and stopping distance? Is it linear? Yes.

What do you think? Will you be able to stop in time to avoid hitting the moose? What are the factors that determine how soon you will be able to stop the car?

Stopping your car What factors affect your car’s stopping ability? Speed Road conditions (dry, wet, oil slicked, dirt, gravel, paved, etc.) Brake condition Tire condition / Type of tires Vehicle weight

Effect of Speed on Stopping Distance As speed increases, does it take longer to stop? Yes. What is the relationship between speed and stopping distance? Is it linear? No

Effect of Speed on Stopping Distance As speed increases, stopping distance increases exponentially as seen in the graph below.

Effect of Speed on Stopping Distance As speed increases, stopping distance increases exponentially as seen in the graph below.

Braking distance game http://www.mrmont.com/games/brakingdistance.html Glowing disk brakes (car stopping) https://www.youtube.com/watch?v=D8MsuFHlc54 Garage disk brake failure (preferred) https://www.youtube.com/watch?v=c_ItwLcBw5Q Russian disk brake failure https://www.youtube.com/watch?v=zV8FWavCzTI

The Mathematical Relationship vf2 – vi2 = 2ad Where: vf and vi are the final and initial velocities, respectively. a = acceleration. d = distance traveled during stopping. The final speed for a vehicle slowing down can be set to zero. The acceleration can be considered to be uniform and constant while the vehicle slows down. The acceleration is negative since the vehicle is slowing down.

The Mathematical Relationship In its simplest form, the stopping distance is related to initial velocity and acceleration as follows: d = v2/2a The acceleration “a” is the rate of braking What are its implications? If the speed doubles, the stopping distance quadruples. If the speed is cut in half, the stopping distance is reduced by one-fourth. What happens if the speed is tripled?

Energy A car’s energy of motion (kinetic energy) is calculated by KE = ½ mv2 As the velocity increases, the energy goes up with the square of the velocity Getting rid of that energy happens at a constant rate – via the brakes. So the energy goes up faster than the brakes can get rid of it. What are its implications? If the speed doubles, the stopping distance quadruples. If the speed is cut in half, the stopping distance is reduced by one-fourth. What happens if the speed is tripled?

Example 1: What does it mean? A car is able to stop in 20 meters when traveling at 30 mph. How much distance will be required before it stops if the vehicle is traveling at: 15 mph? (1/2 of 30 mph) 60 mph? (twice 30 mph) 45 mph? (3x 15 mph) 75 mph? (5x 15 mph) 5 m = ¼ 80 m = 4x 45 m = 9x dstop at 15 mph 125 m = 25x dstop at 15 mph

A Shortcut If you know the base stopping distance to which relates to a given speed/velocity, the stopping distance for any other speed can be determined as follows: d = do x n2 Where: do = original stopping distance n = factor by which the speed at the point where the vehicle stops changes from the speed used to compute the original stopping distance, do.

A Shortcut Example: Using a from example 1: Using b from example 1: do = 20 meters n = ½ (v/vo = 15 mph/30 mph) d = (20 m)(½2) = (20 m)(¼) = 5 meters Using b from example 1: n = 2 (v/vo = 60 mph/30 mph) d = (20 m)(22) = (20 m)(4) = 80 meters

Example 2: Which Car is Safer? Considering the following graph, which car would be safer? Why? Initial Velocity Stopping Distance Car B Car A Car A because its relative stopping distance is better overall for any speed.

Another View https://www.youtube.com/watch?v=Z_n-HIBnfts

Key Ideas The most important factor in determining whether or not you will stop in time to avoid an accident is speed. The distance required to stop is proportional to the square of the speed (d = v2/2a) Response time will increase the distance required to stop.