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Motion in Straight-Line Problem

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Freeway Traffic. According to a Scientific American article (May, 1990), current freeways can sustain about N vehicles per lane per hour in smooth traffic flow at speed . Above that figure the traffic flow becomes "turbulent" (stop-and-go).

1) If a vehicle is of length L on the average, what is the average spacing between vehicles at the above traffic density?

2) Collision-avoidance automated control systems, which operate by bouncing radar or sonar signals off surrounding vehicles and then accelerate or brake the car when necessary, could greatly reduce the required spacing between vehicles. If the average spacing is a distance x (two car lengths), how many vehicles per hour can a lane of traffic carry at speed v?

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Problem on Motion along Straight Line

A helicopter carrying Dr. Evil takes off with a constant upward acceleration of 5.0 m/s^2 . Secret agent Austin Powers jumps on just as the helicopter lifts off the ground. After the two men struggle for 10.0 s, Powers shuts off the engine and steps out of the helicopter. Assume that the helicopter is in free fall after its engine is shut off and ignore effects of air resistance.

What is the maximum height above ground reached by the helicopter?

Powers deploys a jet pack strapped on his back 7.0 s after leaving the helicopter, and then he has a constant downward acceleration with magnitude 2.0 m/s^2. How far is Powers above the ground when the helicopter crashes into the ground?

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