Maximum Speed to Avoid Barrier with Delayed Braking

[CyberSyringe]

Homework Statement

A driver of a car suddenly sees the lights of a barrier 40m ahead. It takes the driver 0.75s before he applies the brakes, and the average acceleration during braking is -10.0m/s^2

What is the maximum speed at which the car could be moving and not hit the barrier 40.0m ahead?

Homework Equations

Vfinal^2 = Vinitial^2 + 2aΔx

The Attempt at a Solution

I attempted to apply the following equation above, but of course due to braking delay of 0.75s the delta x would be different. I have no idea how to apply the two together so I can truly figure out the delta x between the time of braking to figure out what the initial velocity could be given the acceleration to reach a final velocity of 0.

I know somehow that 40m - Vinitial(0.75s) would be the delta x to plug into the above equation.

 

[SteamKing]

You do have to do a little bit of algebra here to find Vinitial. Have you set up the problem symbolically? Remember, if you have an expression for what Δx represents, go ahead and subtitute that into the equation and solve for Vinitial.

 

[CyberSyringe]

I've gotten as far as setting it up to solve for Vinitial, but at this point I am stumped on actually being able to solve the equation.

0 = Vinitial^2 + 2(-10m/s^2)(40m - 0.75sVi)

I don't know how to isolate Vinitial by itself, and the units are also quite confusing.

 

[CyberSyringe]

0 = Vinitial + 15 m/s - 800m^2/s^2

I believe all I do now is quadratic equation and then solve for Vi that way?

 

[SteamKing]

0 = Vinitial + 15 m/s - 800m^2/s^2

I believe all I do now is quadratic equation and then solve for Vi that way?

The only problem is, the expression above is not a quadratic equation. The units are not the same as those for velocity in each quantity in the equation. (You can't add m/s and m^2/s^2 and hope to get a meaningful result.)

I've gotten as far as setting it up to solve for Vinitial, but at this point I am stumped on actually being able to solve the equation.

0 = Vinitial^2 + 2(-10m/s^2)(40m - 0.75sVi)

I don't know how to isolate Vinitial by itself, and the units are also quite confusing.

It is better to work the algebra using symbolic variables only, omitting the units. When the algebra gives you an expression for Vinitial, then you can substitute the known values of the other variables and calculate the value of Vinitial which satisfies the equation.

 

[7Singularity]

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