If you step on your car's brakes hard, the wheels stop turning (i.e., the wheels "lock") after 1.5 revolutions.

At the same constant acceleration, how many revolutions do the wheels make before stopping if your initial speed is twice as high?

wf^2=wi^2+2A*displacement

A= -wi^2/2(1.5rev)

if initial speed is the doubled, then w^2 term in the numerator is x4, so rev must be x4 to keep A constant.

so 4x1.5=6rev

To answer this question, we need to understand the relationship between the initial speed, the number of revolutions, and the stopping distance. Let's break down the steps to find the solution:

Step 1: Understand the initial scenario
In the given scenario, the wheels stop turning after 1.5 revolutions. This means that the stopping distance is equal to 1.5 revolutions.

Step 2: Determine the relationship between initial speed and stopping distance
To understand the relationship between initial speed and stopping distance, let's assume the given scenario has an initial speed of "v". This results in a stopping distance of 1.5 revolutions.

Step 3: Determine the relationship between initial speed and revolutions
Next, we need to determine the relationship between the initial speed and the number of revolutions. From the given scenario, we can infer that as the initial speed increases, the number of revolutions also increases.

Step 4: Analyze the relationship between the initial speed and number of revolutions
Based on the given information, we can assume that the number of revolutions is directly proportional to the initial speed. This means that if we double the initial speed, the number of revolutions should also double.

Step 5: Calculate the number of revolutions for a given scenario
Using the information from step 4, we can calculate the number of revolutions when the initial speed is twice as high. Since the initial speed is doubled, the number of revolutions should also double. Therefore, if the initial scenario had 1.5 revolutions, the new scenario will have 1.5 x 2 = 3 revolutions.

Therefore, if you step on your car's brakes hard with twice the initial speed, the wheels will make 3 revolutions before stopping.