An uncontrolled automobile traveling at 45 mph strikes squarely a highway crash
ID: 1861301 • Letter: A
Question
An uncontrolled automobile traveling at 45 mph strikes squarely a highway crash barrier. After hitting the barrier the automobile decelerates at a rate proportional to the distance x the automobile has moved into the barrier, that is, a = 60 sqrt(x), where a and x are expressed in ft/s2and ft, respectively. Determine the distance the automobile will move into the barrier before it comes to rest.
An uncontrolled automobile traveling at 45 mph strikes squarely a highway crash barrier. After hitting the barrier the automobile decelerates at a rate proportional to the distance x the automobile has moved into the barrier, that is, a = 60 sqrt(x), where a and x are expressed in ft/s2and ft, respectively. Determine the distance the automobile will move into the barrier before it comes to rest.Explanation / Answer
u= 45
a= 60*sqrt(x)------------------(1)
a= vdv/dx
from(1)
60*sqrt(x)=vdv/dx
hence vdv= 60*sqrt(x)dx
integrate both sides we get
(v^2/2) = 60 * (x^3/2) *2/3
45^2/2 = 40 x^3/2
x^3/2 = 25.16
x= 8.58m----------------> answer
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