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

AI Thread Summary
A driver speeding at 65 km/h in a school zone takes significantly longer to stop compared to if they had adhered to the 40 km/h limit. With a reaction time of 0.80 seconds and a braking force of 12,000 N, calculations show that the stopping distance at 65 km/h is 27.25 meters, while at 40 km/h, it is only 10.32 meters. The difference in stopping distance is 16.93 meters, illustrating the dangers of speeding in school zones. The work-energy theorem is applied to derive these distances, emphasizing the importance of reducing speed for safety. This analysis highlights the critical need for drivers to obey speed limits, especially in areas with children.
TalibanNinja
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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.
 
Last edited:
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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.
 
i've tried the question using the knowledge i have but I am not sure.
 
Start by stating the work-energy theorem.
 
Hint: Use \frac{1}{2}mv2=Fd
 

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