You are driving at 22.0 m/s when you suddenly slam on the brakes to avoid a collision. You come to a complete stop. When you stop, your acceleration is determined by your tires and the road conditions, and it is a constant –9.60 m/s2. The skid marks you leave behind can be measured to determine your displacement. How long will your skid marks be?


To solve for the displacement (the length of your skid marks), we can use the following kinematic equation:

\[
v_f^2 = v_i^2 + 2a d
\]

Where:
- \( v_f \) is the final velocity (0 m/s, since you come to a stop),
- \( v_i \) is the initial velocity (22.0 m/s),
- \( a \) is the acceleration (-9.60 m/s²),
- \( d \) is the displacement (the length of the skid marks, which we want to find).

Rearranging the equation to solve for \( d \):

\[
d = \frac{v_f^2 - v_i^2}{2a}
\]

Substitute the known values:

\[
d = \frac{0^2 - (22.0)^2}{2(-9.60)}
\]

Let's calculate this now.It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can still calculate the displacement by following these steps:

1. Square the initial velocity: \( (22.0)^2 = 484 \).
2. Multiply the acceleration by 2: \( 2 \times (-9.60) = -19.2 \).
3. Divide the result of the squared velocity by this number: \( \frac{-484}{-19.2} \approx 25.2 \) meters.

Thus, the length of your skid marks will be approximately 25.2 meters.

Do you want more details or have any questions? Here are 5 related questions:

1. How would the skid mark length change if your initial speed was higher?
2. What happens to the stopping distance if the road is slippery (lower friction)?
3. Can this formula be used for a car slowing down without coming to a full stop?
4. How does constant acceleration affect the time taken to stop?
5. What real-life factors affect the deceleration rate of a vehicle?

**Tip:** Always keep in mind that negative acceleration (deceleration) is used to calculate stopping distances.

You are driving at 22.0 m/s when you suddenly slam on the brakes to avoid a collision. You come to a complete stop. When you stop, your acceleration is determined by your tires and the road conditions, and it is a constant –9.60 m/s2. The skid marks you leave behind can be measured to determine your displacement. How long will your skid marks be?

Learn how to calculate the length of skid marks left by a car when it comes to a stop from an initial speed of 22.0 m/s with a constant acceleration of -9.60 m/s². This problem covers key concepts in kinematics and the use of the constant acceleration formula. Suitable for students in Grades 9-12.

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