To determine the net force acting on the car, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of that object multiplied by its acceleration. The formula is:
[tex]\[ F = m \cdot a \][/tex]
where:
- [tex]\( F \)[/tex] is the net force,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( a \)[/tex] is the acceleration.
### Step-by-Step Solution:
1. Identify the given values:
- Mass of the car, [tex]\( m = 1.2 \times 10^3 \)[/tex] kilograms.
- Initial velocity of the car, [tex]\( u = 0 \)[/tex] meters/second (since the car starts from rest).
- Final velocity of the car, [tex]\( v = 20 \)[/tex] meters/second.
- Time taken to reach the final velocity, [tex]\( t = 5 \)[/tex] seconds.
2. Calculate the acceleration:
The acceleration [tex]\( a \)[/tex] can be found using the formula for acceleration, which is the change in velocity divided by the time taken:
[tex]\[ a = \frac{v - u}{t} \][/tex]
Substitute the known values into the formula:
[tex]\[ a = \frac{20 \, \text{m/s} - 0 \, \text{m/s}}{5 \, \text{s}} \][/tex]
[tex]\[ a = \frac{20 \, \text{m/s}}{5 \, \text{s}} \][/tex]
[tex]\[ a = 4 \, \text{m/s}^2 \][/tex]
3. Calculate the net force:
Using the calculated acceleration and the mass of the car, substitute these values into the formula for force:
[tex]\[ F = m \cdot a \][/tex]
[tex]\[ F = (1.2 \times 10^3 \, \text{kg}) \times (4 \, \text{m/s}^2) \][/tex]
[tex]\[ F = 4.8 \times 10^3 \, \text{N} \][/tex]
Therefore, the net force that acted on the car to cause the acceleration is [tex]\( 4.8 \times 10^3 \)[/tex] newtons. Thus, the correct answer is:
[tex]\[ \boxed{\text{D. } 4.8 \times 10^3 \text{ newtons}} \][/tex]
