If the brakes on a car give the car a constant negative acceleration of 24 m/s2, where k is a positive constant. What is the greatest speed it may be going if it is necessary to be able to stop the car within 25 meters after the brakes are applied?

If the brakes on a car give the car a constant negative acceleration of 24 m/s2, where k is a positive constant. What is the greatest speed it may be going if it is necessary to be able to stop the car within 25 meters after the brakes are applied?

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter2: Motion In One Dimension

Section: Chapter Questions

Problem 2.2OQ: A racing car starts from rest at t = 0 and reaches a final speed at time t. II the acceleration of...

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Very large accelerations can injure the body, especially if they last for a considerable length of time. One model used to gauge the likelihood of injury is the severity index (??), defined as ??=?^5/2?. In the expression, ?t is the duration of the acceleration, but ?a is not equal to the acceleration. Rather, ?a is a dimensionless constant that equals the number of multiples of ?g that the acceleration is equal to. In one set of studies of rear-end collisions, a person's velocity increases by 17.5 km/h17.5 km/h with an acceleration of 30.5 m/s230.5 m/s2 . Let the +?+x direction point in the direction the car is traveling. What is the severity index for the collision? How far ?d does the person travel during the collision if the car was initially moving forward at 4.60 km/h4.60 km/h ?
e rocket-driven sled Sonic Wind No. 2, used for investigating the physiological effects of large accelerations, runs on a straight, level track 1070 m (3500 ft) long. Starting from rest, it can reach a speed of 224 m/s(500 mi/h) in 0.900 s. (a) Compute the acceleration in m/s, assuming that it is constant. (b) What is the ratio of this acceleration to that of a freely falling body (8)? (c) What distance is covered in 0.900 s? (d) A magazine article states that at the end of a certain run, the speed of the sled de- creased from 283 m/s (632 mi/h) to zero in 1.40 s and that during this time the magnitude of the acceleration was greater than 40g. Are these figures consistent?
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