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What is the answer to this physics problem?
In designing a freeway on-ramp, you must make it long enough for cars to be able to accelerate and merge safely with traffic traveling at speeds of 70.0 mph. For an off-ramp, the cars must be able to come to a stop from 70.0 mph over the length of the ramp. Your traffic engineers provide the following data: Powerful cars can accelerate from rest to 60.0 mph in 5.00 s, while less powerful cars take twice as long to do this. When slowing down from 60.0 mph, a car with good tire treads will take 12.0 s to stop, whereas one with bald tires takes 20.0 s.
In order to safely accommodate all the types of vehicles, what should be the minimum length (in meters) of on-ramps?
In order to safely accommodate all the types of vehicles, what should be the minimum length (in meters) of off-ramps?
pherephe...
In designing a freeway on-ramp, you must make it long enough for cars to be able to accelerate and merge safely with traffic traveling at speeds of 70.0 mph. For an off-ramp, the cars must be able to come to a stop from 70.0 mph over the length of the ramp. Your traffic engineers provide the following data: Powerful cars can accelerate from rest to 60.0 mph in 5.00 s, while less powerful cars take twice as long to do this. When slowing down from 60.0 mph, a car with good tire treads will take 12.0 s to stop, whereas one with bald tires takes 20.0 s.
In order to safely accommodate all the types of vehicles, what should be the minimum length (in meters) of on-ramps?
In order to safely accommodate all the types of vehicles, what should be the minimum length (in meters) of off-ramps?
Speed S = 70 miles/h = 0.0194 miles/s
Car specification = 60 miles/h = 0.0167 miles/s
The design of the on-ramp and off-ramp
1.Must be based on the slower car or less powerful
2.Tire will base on the bald.
T(70) = Time to reach 0.0194 m/s
T(70) / Speed (70) = Time to attain Speed (60) / Speed (60 m/h)
T(70) / 0.0194 = 10 s / 0.0167 m/s
T(70) = 0.194 / 0.0167
T(70) = 11.62 sec
Before the Speed is reach the car has already traveled = D(60)
S(60) = speed at 60 (0.0167 m/s)
Ss = starting Speed = 0
S(60) = Ss + at
0.0167 = 0 + a(10)
a = 0.00167 m/sec²
D(0-60) = distance travel From 0 to 60 mph
D(0-60) = Ss(t) + ½ (a)t²
D(0-60) = 0(10) + ½(0.00167)(10)²
D(0-60) = 0.084 miles
Distance traveled for 60 to 70 = D(70)
D(60-70) =Distance traveled for m 60 m/2 to 70 m/s
D(60-70) = S(60)(T(70)) + ½ (a)(T(70))²
D(60-70) = (0.0167)(11.62) + ½(0.00167)(11.62)²
D(60-70) = (0.195) + 0. 1128
D(60-70) = 0.31 miles
DT(70) =How long the 70 m/h speed stop (Off-ramp)
Getting the equivalent time for 70 m/h
T(70 )s / S(70) = 20 s / S(60)
T(70) = (20) S(70) / S(60)
T(70) = (20) (0.0194) / (0.0167)
T(70) = 23.23 sec
Speed final = Speed initial + acceleration (70) (time at 70)
0 = 0.0194 + acceleration (70) T(70)
Acceleration(70) = - 0.0194 / 23.23
Acceleration(70) = - 0.000835 m/sec²
The distance of the Off –ramp = DT(70)
DT(70) = S(70)t + ½ acceleration(70) T(70)²
DT(70) = 0.0194 (23.23) + ½ (-0.000835)(23.23)²
DT(70) = 0.451 – 0.23
DT(70) = 0.185 m
Summary:
minimum length (in meters) of on-ramps:
Distance on the Freeway on-ramp = Distance traveled form start to 60 mph + Distance traveled from 60 to 70 mph
Distance on the Freeway on-ramp = D(0-60) + D(60-70)
Distance on the Freeway on-ramp = 0.084 + 0.31 m
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Distance on the Freeway on-ramp = 0.394 miles or 633.95 meter ◄ Ans
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the minimum length (in meters) of off-ramps?
Distance on the Freeway off-ramp = DT(70)
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Distance on the Freeway off-ramp = 0.185 miles or 297.67 meters ◄ Ans
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Note; 1mile = 1609 meters
Hope this helps
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