To solve this problem, we can use one of the equations of motion, specifically:

$v^2 = u^2 + 2as$

where:

• $v$ is the final velocity (0 m/s, since the car skids to a halt),
• $u$ is the initial velocity (which we want to find),
• $a$ is the acceleration ($-9.4 \, \text{m/s}^2$),
• $s$ is the distance ($34 \, \text{m}$).

Step-by-Step Solution

1. Substitute the values into the equation:

   $0 = u^2 + 2 \cdot (-9.4) \cdot 34$

2. Simplify the equation:

   $0 = u^2 - 638.4$

3. Add $638.4$ to both sides:

   $u^2 = 638.4$

4. Take the square root of both sides:

   $u = \sqrt{638.4}$

5. Calculating $u$:

   $u \approx 25.27 \, \text{m/s}$

Answer

The speed of the car when it slammed on the brakes was approximately 25.27 m/s.

Would you like a more detailed explanation, or do you have any questions?

Here are five related questions to deepen understanding:

1. How would the initial speed change if the skid marks were longer?
2. What would be the initial speed if the acceleration rate changed to $-8.0 \, \text{m/s}^2$?
3. If the car took 4 seconds to stop, what was its average speed during this time?
4. How would we calculate the stopping distance if we knew the initial speed and deceleration?
5. How can we calculate the time it took for the car to stop with the given data?

Tip: In problems involving stopping or deceleration, setting the final velocity to zero helps simplify calculations.