The question provided asks for the length of skid marks left when a car decelerates to a stop, given initial speed, constant acceleration, and using the formula:

$v_f^2 = v_i^2 + 2ad$

Given:

• $v_i = 22.0 \, \text{m/s}$ (initial velocity)
• $v_f = 0 \, \text{m/s}$ (final velocity, since the car stops)
• $a = -9.60 \, \text{m/s}^2$ (negative acceleration due to deceleration)

We need to find the displacement ($d$) or the length of the skid marks.

Rearranging the formula for displacement:

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

Substituting the known values:

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

$d = \frac{-484}{-19.2}$

$d = 25.2 \, \text{m}$

So, the length of the skid marks is 25.2 meters (Option B).

Would you like further details or have any questions?

Related Questions:

1. How would the length of the skid marks change if the initial velocity was 30 m/s?
2. What if the acceleration was doubled, how would that affect the skid marks length?
3. How is this formula derived from basic kinematic equations?
4. What are the safety implications of understanding such deceleration distances?
5. How would the skid marks change if the car did not come to a full stop but slowed to 5 m/s?

Tip: Always ensure you correctly account for the sign of acceleration when applying kinematic equations!