Stopping Your Car

1
Stopping Your Car

• Transportation Ch. 1, Act. 3

2
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

3
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?

4
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.

5
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?

6
Stopping your car

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

7
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

8
Effect of Speed on Stopping Distance

• As speed increases, stopping distance increases
  exponentially as seen in the graph below.

9
Effect of Speed on Stopping Distance

• As speed increases, stopping distance increases
  exponentially as seen in the graph below.

10
Braking distance gamehttp//www.mrmont.com/games
/brakingdistance.html

• Glowing disk brakes (car stopping)
• https//www.youtube.com/watch?vD8MsuFHlc54
• Garage disk brake failure (preferred)
• https//www.youtube.com/watch?vc_ItwLcBw5Q
• Russian disk brake failure
• https//www.youtube.com/watch?vzV8FWavCzTI

11
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.

12
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?

13
Energy

• A cars 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?

14
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)

15
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.

16
A Shortcut

• Example
• Using a 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
• do 20 meters
• n 2 (v/vo 60 mph/30 mph)
• d (20 m)(22) (20 m)(4) 80 meters

17
Example 2 Which Car is Safer?

• Considering the following graph, which car would
  be safer? Why?

Car A because its relative stopping distance is
better overall for any speed.
18
Another View

• https//www.youtube.com/watch?vZ_n-HIBnfts

19
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.