How Do You Calculate Freeway Carrying Capacity with Kinematics?

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To calculate the freeway carrying capacity, the average speed of 90 km/h, car length of 6.0 m, and a distance of 65 m between cars are used. Each car occupies 71 m (6 m + 65 m), and with a 90 km stretch, the number of cars per lane is determined to be 3800 per hour. The discussion also includes a scenario where a woman must decide whether to stop or accelerate through a yellow light, given her speed, distance to the intersection, and deceleration capabilities. Kinematic equations are suggested for solving this problem. Understanding these concepts is essential for applying physics to real-world driving situations.
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How would you solve this...

Calculate the carrying capacity (number of cars passing a given point per hour) on a freeway with three lanes (in one direction) using the following assumptions: the average speed is 90 km/h. the average length of a car is 6.0m, and the average distance between cars should be 65m.

ANS: 3800/hr.

I'm really stuck at this question. Somebody please help, we are currently studying velocity and acceleration in Physics.
 
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smbascug said:
Calculate the carrying capacity (number of cars passing a given point per hour) on a freeway with three lanes (in one direction) using the following assumptions: the average speed is 90 km/h. the average length of a car is 6.0m, and the average distance between cars should be 65m.

The car which is at 90 km distance from the given point would just pass. All the other cars, closer than that farthest one woud obviously pass, too. One car occupies 6 + 65 m length. How many cars are then there in 90 km length of one lane?

ehild
 
Another one...

Thank you very much i got the first one. Physics isn't my strong point because i might not really good with word problems.


A woman driving her car at 50 km/h approaches an intersection when the traffic lights turns yellow. She knows that the yellow ligh last only 2.0s before turning to red. and she is 30 m away from the near side of the intersection. Should she try to stop or should she make a run for it? The intersection is 12m wide. and her car's maxium deceleration is - 6.0 m/s*s. also her car takes 7.0 s to accelerate from 50 km/h to 70 km/h. Ignor the length of her car and her reaction time.
 
You need to use some kinematic equations. Can you apply the correct ones?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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