To determine how far the car travels while decelerating, let’s follow these steps:
### 1. Identify the Known Variables:
- Initial velocity ([tex]\(v_i\)[/tex]): 32 m/s (north)
- Acceleration ([tex]\(a\)[/tex]): -8 m/s²
- Time ([tex]\(t\)[/tex]): 4 seconds
### 2. Calculate the Final Velocity:
First, we need to find the final velocity ([tex]\(v_f\)[/tex]) of the car after 4 seconds using the formula:
[tex]\[ v_f = v_i + a \cdot t \][/tex]
Substitute the known values:
[tex]\[ v_f = 32 + (-8) \cdot 4 \][/tex]
[tex]\[ v_f = 32 - 32 \][/tex]
[tex]\[ v_f = 0 \, \text{m/s} \][/tex]
The final velocity of the car after 4 seconds is 0 m/s, meaning the car comes to a stop.
### 3. Calculate the Displacement:
Now, let’s find the displacement ([tex]\(s\)[/tex]), which is the distance the car travels during these 4 seconds. We use the displacement formula for uniformly accelerated motion:
[tex]\[ s = v_i \cdot t + \frac{1}{2} a \cdot t^2 \][/tex]
Substitute the known values into this formula:
[tex]\[ s = 32 \cdot 4 + \frac{1}{2} \cdot (-8) \cdot 4^2 \][/tex]
[tex]\[ s = 128 + \frac{1}{2} \cdot (-8) \cdot 16 \][/tex]
[tex]\[ s = 128 + (-64) \][/tex]
[tex]\[ s = 128 - 64 \][/tex]
[tex]\[ s = 64 \, \text{meters} \][/tex]
### Conclusion:
The car travels 64 meters during the 4 seconds before it comes to a stop.
