using the GRESA method, try answering the following: A race car accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. Determine the acceleration of the car and the distance traveled.

Let's solve the problem using the GRESA method.

### **GRESA Method:**

1. **Given:**
   - Initial velocity (\(v_i\)) = 18.5 m/s
   - Final velocity (\(v_f\)) = 46.1 m/s
   - Time (\(t\)) = 2.47 s

2. **Required:**
   - The acceleration (\(a\)) of the car
   - The distance traveled (\(d\)) during this time

3. **Equation:**
   - To find acceleration (\(a\)), use the first equation of motion:
   \[
   v_f = v_i + a \cdot t
   \]
   - To find distance (\(d\)), use the second equation of motion:
   \[
   d = v_i \cdot t + \frac{1}{2} a \cdot t^2
   \]

4. **Solution:**

   **Step 1: Find the Acceleration (\(a\))**
   - Substitute the given values into the first equation of motion:
   \[
   46.1 = 18.5 + a \cdot 2.47
   \]
   - Solve for \(a\):
   \[
   46.1 - 18.5 = a \cdot 2.47
   \]
   \[
   27.6 = a \cdot 2.47
   \]
   \[
   a = \frac{27.6}{2.47} \approx 11.17 \text{ m/s}^2
   \]

   **Step 2: Find the Distance Traveled (\(d\))**
   - Now that we have \(a = 11.17 \, \text{m/s}^2\), substitute it back into the second equation of motion:
   \[
   d = 18.5 \cdot 2.47 + \frac{1}{2} \cdot 11.17 \cdot (2.47)^2
   \]
   - Simplify:
   \[
   d = 45.695 + \frac{1}{2} \cdot 11.17 \cdot 6.1009
   \]
   \[
   d = 45.695 + 34.0868
   \]
   \[
   d \approx 79.78 \, \text{meters}
   \]

5. **Answer:**
   - The acceleration of the car is approximately **11.17 m/s²**.
   - The distance traveled by the car is approximately **79.78 meters**.

Would you like more details, or do you have any questions?

### **Relative Questions:**
1. How would the acceleration change if the car took twice as long to reach the final velocity?
2. What formula should be used if the distance traveled was given instead of time?
3. Can you calculate the final velocity if the acceleration and distance are known?
4. What would happen to the distance traveled if the initial velocity was zero?
5. How can you determine the average velocity of the car during this time?

**Tip:** When working with equations of motion, carefully identify which variables are given and choose the equation that directly relates them to the unknown variable.

Learn how to calculate the acceleration and distance traveled by a race car using the GRESA method. Solve the problem step-by-step with initial velocity, final velocity, and time given. Discover the equations of motion used and understand the concepts of uniform acceleration. Suitable for high school students and anyone interested in physics and mechanics.

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