How Much Longer Does It Take to Stop When Speeding in a School Zone?

F.In summary, the problem involves a driver who ignores the reduced speed limit in a school zone and continues at a higher speed. The question asks how many more meters it will take for the driver to stop compared to if he had reduced his speed. Using the work-energy theorem, and assuming a good reaction time and a constant braking friction, it can be calculated that the driver will take approximately 16.93 meters longer to stop at the higher speed.
  • #1
TalibanNinja
15
0

Homework Statement


A driver carelessly ignores the reduced speed limit of 40.0 km/h in a school zone and continues at 65 km/h. Assuming a good reaction time of 0.80 s, how many more metres will it take him to stop than if he had reduced his speed? Assume 2000kg car has a constant braking friction of 12000N. (Must use work-energy theorem)
va=11.11m/s
vb=18.05ms
Ff=12000N
m=2000kg
g=9.8m/s^2

Homework Equations



Ff=μFn
Work done to an object = change in kinetic energy
Wf=Ek
μmgd=1/2mv^2
d=v^2/2μg

The Attempt at a Solution




μ=Ff/Fn
μ=12000N/(2000kg*9.8m/s^2)
μ=0.61

da=(11.11m/s)^2/2*(0.61)(9.8m/s^2)
da=10.32m

db=(18.05m/s)^2/2*(0.61)(9.8m.s^2)
db=27.25m

Δd=db-da
Δd=27.25m - 10.32m
Δd=16.93

Therefore it takes the driver 16.93m longer to stop than if he slowed his speed.
 
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  • #2
You must show us an attempt at a solution first before we are allowed to help you. First try to write an equation for distance if he had slowed down to 40km/h.
 
  • #3
i've tried the question using the knowledge i have but I am not sure.
 
  • #4
Start by stating the work-energy theorem.
 
  • #5
Hint: Use [itex]\frac{1}{2}[/itex]mv2=Fd
 

1. What is stopping distance speed?

Stopping distance speed refers to the speed at which a vehicle can come to a complete stop, taking into account both the time and distance required to do so.

2. How is stopping distance speed calculated?

Stopping distance speed is calculated by adding the reaction time of the driver, the braking distance of the vehicle, and the distance traveled during the reaction time.

3. What factors affect stopping distance speed?

The factors that affect stopping distance speed include the speed of the vehicle, the condition of the road surface, the condition of the tires, the weight of the vehicle, and weather conditions such as rain or snow.

4. How can stopping distance speed be reduced?

Stopping distance speed can be reduced by maintaining a safe driving speed, maintaining proper tire pressure and tread, and ensuring that the vehicle's brakes are in good working condition. In addition, increasing following distance and avoiding distractions while driving can also help reduce stopping distance speed.

5. Why is understanding stopping distance speed important?

Understanding stopping distance speed is important for safe driving and preventing accidents. It allows drivers to adjust their speed and maintain a safe following distance to avoid collisions and ensure the safety of themselves and others on the road.

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