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I have a question about the set-up for an equation. The question is: "The driver of a car going 98.0 km/h suddenly sees the lights of a barrier 45.0 m ahead. It takes the driver 0.75 s to apply the brakes, and the average acceleration during braking is -10.0 m/s^2. I need to know the maximum speed that the car can be going to not hit the barrier 45 m ahead assuming acceleration doesn't change. I've set up the "translation" of changing all of the numbers into variables but I'm not too sure where to put them.

Hello Doug,

I don't understand what you mean by "changing all of the numbers into variables", so I'll show you how I would work it.

First, we will need the speed in m/s.

98.0 km/h * (1000 m/1 km) * (1 h/3600 s) = 27.22 m/s

During the reaction time, the car will travel

27.22 m/s * 0.75 s = 20.42 m

So the deceleration phase needs to stop the car in 45.0 m - 20.42 m = 24.58 m

Then I thought I would see if the car will stop without hitting the barrier. To see if it does, use the kinematic formula

Vf^2 = Vi^2 + 2*a*x

where Vf = 0, Vi = 27.22 m/s, and a = -10.0 m/s^2.

0 = (27.22 m/s)^2 + 2*(-10.0 m/s^2)*x

2*(+10.0 m/s^2)*x = (27.22 m/s)^2

x = (27.22 m/s)^2 / 2*(+10.0 m/s^2) = 37.04 m

So, 98 km/h is too fast. (Note: the work in this paragraph wasn't really necessary to find the answer to the given problem.)

To see what speed will just barely be low enough, Leave Vi as a variable and put 24.58 m in for x.

Vf^2 = Vi^2 + 2*a*x

0 = Vi^2 + 2*(-10.0 m/s^2)*24.58 m

Vi^2 = 2*(+10.0 m/s^2)*24.58 m

I will leave the rest for you to do. It may be that your instructor would expect you to change the units of the result back to km/h. You know your instructor better than I do.

I hope this helps,

Steve

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