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 2.91 s, and the velocity of the car decreases to +4.88 m/s. The car's deceleration has a magnitude of 2.74 m/s? during this time. What is the car's displacement?

To solve this problem, we need to find the displacement of the car while it is decelerating. We can use the following kinematic equation, which relates initial velocity, final velocity, acceleration, time, and displacement:

\[
\text{Displacement} (s) = v_i t + \frac{1}{2} a t^2
\]

Where:
- \(v_i\) is the initial velocity (which we need to find),
- \(v_f\) is the final velocity (given as \(+4.88 \, \text{m/s}\)),
- \(a\) is the acceleration (which is negative because it's a deceleration, so \(a = -2.74 \, \text{m/s}^2\)),
- \(t\) is the time (given as \(2.91 \, \text{s}\)),
- \(s\) is the displacement (what we want to find).

### Step 1: Find the Initial Velocity
We can first use the equation that relates initial and final velocity with acceleration and time:

\[
v_f = v_i + at
\]

Substituting the known values:

\[
4.88 \, \text{m/s} = v_i + (-2.74 \, \text{m/s}^2)(2.91 \, \text{s})
\]

Solving for \(v_i\):

\[
v_i = 4.88 \, \text{m/s} + (2.74 \, \text{m/s}^2 \times 2.91 \, \text{s})
\]

\[
v_i = 4.88 \, \text{m/s} + 7.97 \, \text{m/s}
\]

\[
v_i = 12.85 \, \text{m/s}
\]

### Step 2: Calculate the Displacement
Now that we have \(v_i\), we can use the displacement equation:

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

Substituting the values:

\[
s = (12.85 \, \text{m/s})(2.91 \, \text{s}) + \frac{1}{2}(-2.74 \, \text{m/s}^2)(2.91 \, \text{s})^2
\]

Calculating each term:

\[
s = 37.40 \, \text{m} + \frac{1}{2}(-2.74 \, \text{m/s}^2)(8.47 \, \text{s}^2)
\]

\[
s = 37.40 \, \text{m} - 11.61 \, \text{m}
\]

\[
s = 25.79 \, \text{m}
\]

### Final Answer:
The car's displacement during this time is **25.79 meters**.

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Do you want further details or have any questions?

Here are some related questions:
1. How do you calculate acceleration if you know the initial and final velocities and the displacement?
2. What would happen to the displacement if the car's deceleration was greater?
3. How does the kinematic equation change if the car was accelerating instead of decelerating?
4. What is the difference between displacement and distance in physics?
5. How can we determine the stopping distance of a car given its initial speed and deceleration?

**Tip:** Always keep track of the signs when dealing with acceleration or deceleration to avoid errors in your calculations.

Learn how to calculate the displacement of a car during deceleration using kinematic equations. This physics problem involves finding displacement from given initial and final velocities, deceleration, and time. Detailed step-by-step solution included.

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