I need help finding how far the car will skid
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I need help finding how far the car will skid

[From: ] [author: ] [Date: 11-07-09] [Hit: ]
same constant braking force?-The work done on the car (by the friction in the road) equals the loss of kinetic energy in the car.From that you can see that the distance is proportional to the square of the speed; so if the speed gets doubled, the braking distance gets quadrupled; etc.Then apply it to the second case,If you STILL need help:Divide the second equation by the first equation.......
A car is moving 15 m/s skids to a stop in 20m. If the car travels at 45 m/s. How far will it skid, assuming .. same constant braking force?

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The work done on the car (by the friction in the road) equals the loss of kinetic energy in the car.

work done on car = loss of KE
force × distance = ½(mass)v²

From that you can see that the distance is proportional to the square of the speed; so if the speed gets doubled, the braking distance gets quadrupled; etc.

If you still need help: apply that equation to the first case (the first skid):
F × (20meters) = ½(mass)(15meters/s)²

Then apply it to the second case, using the variable "d" to stand for the unknown distance:
F × (d) = ½(mass)(45meters/s)²

Now you can use algebra to combine those two equations and solve for "d"

If you STILL need help: Divide the second equation by the first equation. That gives you:
d / (20meters) = (45meters/s)² / (15meters/s)²

Multiply both sides by "20meters" to get:
d = (20meters) × (45meters/s)² / (15meters/s)²

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W = FΔD = ΔKE
(-F)ΔD = 1/2 m(vf)^2 - 1/2 m(vi)^2

Note: The breaking force is opposite the direction of motion so there is a -F. Also, since the final velocity is zero (the car comes to a stop), 1/2 m(vf)^2 = 0

-maΔD = - 1/2 m(vi)^2
aΔD = 1/2 (vi)^2
a = (vi)^2 / (2ΔD)
a = (15 m/s)^2 / (2*20 m) = 5.625 m/s/s

Since the same breaking force is applied in the second scenario, the acceleration (or deceleration for that matter) is the same.

ΔD = (vi)^2 / (2a)
ΔD = (45 m/s)^2 / (2*5.625 m/s/s) = 180 m

The car skids 180 m

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Kinetic Energy = 0.5Mv^2 = Work = Force * distance

M is constant ===> Energy is a function of v^2 =====> We tripled v ===> Energy increased by 3^2 = 9 times the energy at 45 m/s

Work was increased by 9 times

Force is constant ===> Distance must increase by 9 times

D = 9 * 20 = 180 m
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