Find minimum stopping distance of a car

[evan b]

1. Homework Statement

It takes a minimum distance of 66.64 m to stop a car moving at 14.0 m/s by applying the brakes (without locking the wheels). Assume that the same frictional forces apply and find the minimum stopping distance, when the car is moving at 32.0 m/s.

The Attempt at a Solution

i'm confused on what to do here... i thought it might be as simple as setting them equal to each other and solving for the distance. we know the mass of the car is the same so that isn't a factor. for the first we know Vi=14 m/s and Vf = 0, and the second time its velocity is Vi=32 m/s and Vf = 0. I'm not sure where to go from here...

 

[heth]

Which equations do you think might be useful?

 

[thomate1]

As a scientist, the first step in solving this problem would be to identify and define the variables involved. We know that the minimum stopping distance (d) is equal to 66.64 m when the initial velocity (Vi) is 14.0 m/s. We also know that the final velocity (Vf) is 0 m/s and that the frictional forces are the same in both cases.

Next, we can use the formula d = (Vi^2 - Vf^2) / 2a, where a is the acceleration of the car due to the frictional forces. Since we are assuming the same frictional forces in both cases, we can set the two equations equal to each other and solve for the acceleration (a).

66.64 = (14^2 - 0^2) / 2a and d = (32^2 - 0^2) / 2a

Solving for a in both equations, we get a = 3.08 m/s^2. Now, we can plug this value back into either equation to solve for the minimum stopping distance when the initial velocity is 32.0 m/s.

d = (32^2 - 0^2) / 2(3.08) = 166.45 m

Therefore, the minimum stopping distance for a car moving at 32.0 m/s is 166.45 m. This calculation assumes that the car is braking without locking the wheels and that the frictional forces remain constant. It is important to note that in real-life situations, other factors such as road conditions and reaction time of the driver may affect the stopping distance of a car.