 Refer to multiple-concept example 5 to review a method by which this problem can be solved. You are driving your car, and the traffic light ahead turns red. You apply the brakes for 3.00 s, and the velocity of the car decreases 4.5m / s The car's deceleration has a magnitude of 2.70m / (s ^ 2) during this time. What is the car's displacement? 

To solve the problem, we need to calculate the car's displacement during the braking period. We are given:

- The initial velocity decrease: \( \Delta v = 4.5 \, \text{m/s} \)
- Time of braking: \( t = 3.00 \, \text{s} \)
- Magnitude of deceleration: \( a = 2.70 \, \text{m/s}^2 \)

We can use the following kinematic equation to find the displacement:

\[
\Delta x = v_i t + \frac{1}{2} a t^2
\]

However, first, we need to find the initial velocity \( v_i \), which is the velocity before the brakes were applied.

### Step 1: Find the initial velocity \( v_i \)

We know that:

\[
v_f = v_i - a t
\]

Since \( v_f = v_i - 4.5 \, \text{m/s} \) and \( v_f = 0 \, \text{m/s} \) (because the car comes to a stop), we can solve for \( v_i \):

\[
v_i = 4.5 \, \text{m/s}
\]

### Step 2: Calculate the displacement \( \Delta x \)

Now, we substitute the known values into the kinematic equation:

\[
\Delta x = v_i t + \frac{1}{2} a t^2
\]

Substituting the values:

\[
\Delta x = (4.5 \, \text{m/s})(3.00 \, \text{s}) + \frac{1}{2}(2.70 \, \text{m/s}^2)(3.00 \, \text{s})^2
\]

### Step 3: Perform the calculations

Calculate the first term:

\[
4.5 \, \text{m/s} \times 3.00 \, \text{s} = 13.5 \, \text{m}
\]

Calculate the second term:

\[
\frac{1}{2} \times 2.70 \, \text{m/s}^2 \times (3.00 \, \text{s})^2 = 0.5 \times 2.70 \times 9 = 12.15 \, \text{m}
\]

Now, add the two results:

\[
\Delta x = 13.5 \, \text{m} + 12.15 \, \text{m} = 25.65 \, \text{m}
\]

So, the car's displacement during the braking period is **25.65 meters**.

Would you like more details or have any questions?

Here are 5 related questions you might consider:
1. What would happen to the displacement if the braking time was shorter?
2. How would the displacement change if the deceleration was greater?
3. Can this method be used to calculate displacement if the initial velocity is not given directly?
4. What role does friction play in the braking process?
5. How do different road conditions (wet, dry, icy) affect the car’s deceleration and displacement?

**Tip:** When analyzing motion problems, always consider the direction of acceleration (or deceleration) relative to the initial velocity to determine whether the object is speeding up or slowing down.

Learn how to calculate the displacement of a car during braking using kinematic equations. This problem involves determining displacement given initial velocity, time of braking, and deceleration magnitude. Suitable for high school physics students.

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