The braking distance of a car can be modeled by d=s+(s^2/10) where d is the distance (in feet) that the car travels before coming to a stop, and s is the speed at which the car is traveling (miles per hour). Find the speed that results in a braking distance of 90 feet.

In order to solve this problem, we must start by setting the given equation equal to the 90 feet you have available to stop the car, so the equation will then look like this:

[tex]\frac{s^{2}}{10}+s=90[/tex]

we can then move everything to the left side of the equation so we get:

[tex]\frac{s^{2}}{10}+s-90=0[/tex]

we can now multipy both sides of the equation by 10 so we get:

[tex]s^{2}-10s-900=0[/tex]

Next, we can solve this equation by using the quadratic formula, so we get:

[tex]s=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex]

and then we input the values:

[tex]s=\frac{-10\pm \sqrt{(10)^{2}-4(1)(900)}}{2(1)}[/tex]

and solve:

[tex]s=\frac{-10\pm \sqrt{3700}}{2}[/tex]

this gives us two answers:

s=-35.41mph

s=25.41mph

we pick the first answer since we will assume the disceleration goes in the negative direction, so we get:

s=25.41mph

shubhamchouhanvrVT shubhamchouhanvrVT · Answer 2 · 2022-07-04T10:15:18+02:00

The speed that results in a braking distance of 90 feet will be s=25.41mph

What is speed?

Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.

In order to solve this problem, we must start by setting the given equation equal to the 90 feet you have available to stop the car, so the equation will then look like this:

we can then move everything to the left side of the equation so we get:

[tex]\dfrac{s^2}{10}+s = 90[/tex]

we can now multiply both sides of the equation by 10 so we get:

[tex]s^2 -10s-900 = 0[/tex]

Next, we can solve this equation by using the quadratic formula, so we get:

[tex]s = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

and then we input the values:

[tex]s =\dfrac{-10\pm\sqrt{10^2-(4\times (1)\times 900}}{2}[/tex]

and solve:

[tex]s=\dfrac{-10\pm\sqrt{3700}}{2}[/tex]

This gives us two answers:

s =-35.41mph

s = 25.41mph

we pick the first answer since we will assume the deceleration goes in the negative direction, so we get:

s = 25.41mph

Therefore the speed that results in a braking distance of 90 feet will be s=25.41mph

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