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23 Nov 2019

The stopping distance of a vehicle is an important safety factor.Assuming a constant braking force, use the work-energy theorem toshow that a vehicle's stopping distance is proportional to thesquare of its initial speed. If an automobile traveling at 45 km/his brought to a stop in 50 m, what would be the stopping distancefor an initial speed of 90 km/h?

Answer: 200 m

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Patrina Schowalter
Patrina SchowalterLv2
18 Oct 2019

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

A car with a mass of 1300 kg is initially moving at a speed of 40 km/h when the brakes are applied and the car is brought to a stop in 15 m. Assuming that the force that stops the car is constant, find (a) the magnitude of that force and (b) the time required for the change in speed. If the initial speed is doubled and the car experiences the same force during the braking, by what factors are (c) the stopping distance and (d) the stopping time multiplied?

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(Answer is 15.5m/s)

The body of a car with a mass, m, is designed to have a crumplezone that will collapse by a length, d, to absorb the force ofimpact in a head-on collision.

A) if the car, driving straight at a wall when it is traveling atan initial velocity, v, how much energy is lost in thecollision?


B) Assume the entire crumple length, d, is used to stop the car.Using work-energy equivalence, find the force needed to stop thecar in terms of m, v, and d. Assume the force stays constant.

C) How much power is used by the stopping force the moment afterthe car impacts the wall? Express your answer in terms of m, v, andd.

d) if the car is moving at 3v instead of v at the time of impact,find the force, F3, needed to stop the car in a distance, d.

E) if a combination of a crumple zone and a guard rail backed by aspring of spring constant, k, are used to stop the car, neither hasto do much work. imagine that half the energy of the car isabsorbed by the spring, and that the car stops by compressing thespring a distance, d/2. Using your values from parts (a) and (b),what is the spring constant, k, in terms of m, v, and d?

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