Sure, let's solve the problem step-by-step.
### Step 1: Identify Given Values
- Initial Velocity ([tex]\(v_i\)[/tex]): 35 m/s
- Final Velocity ([tex]\(v_f\)[/tex]): 65 m/s
- Time ([tex]\(t\)[/tex]): 5 seconds
### Step 2: Understand the Formula
We need to find the acceleration ([tex]\(a\)[/tex]). The formula to calculate acceleration when initial velocity, final velocity, and time are given is:
[tex]\[ a = \frac{{v_f - v_i}}{t} \][/tex]
### Step 3: Plug in the Values
Substituting the given values into the formula:
[tex]\[ a = \frac{{65 \, \text{m/s} - 35 \, \text{m/s}}}{5 \, \text{s}} \][/tex]
### Step 4: Perform the Calculation
First, determine the difference in velocity:
[tex]\[ 65 \, \text{m/s} - 35 \, \text{m/s} = 30 \, \text{m/s} \][/tex]
Next, divide the change in velocity by the time:
[tex]\[ a = \frac{30 \, \text{m/s}}{5 \, \text{s}} = 6 \, \text{m/s}^2 \][/tex]
### Step 5: Provide the Answer
The correct answer is [tex]\( 6 \, \text{m/s}^2 \)[/tex]. Therefore, the car's acceleration is:
[tex]\[ 6 \, \text{m/s}^2 \][/tex]
So, the correct option is:
[tex]\[ \boxed{6 \, \text{m/s}^2} \][/tex]
