To determine the magnitude of force required to accelerate a car, we can employ Newton's Second Law of Motion which states:
[tex]\[ F = m \cdot a \][/tex]
Where:
- \( F \) is the force,
- \( m \) is the mass of the car,
- \( a \) is the acceleration.
Given:
- The car's mass \( m = 1.7 \times 10^3 \) kilograms,
- The acceleration \( a = 4.75 \) meters/second\(^2\).
Substitute the given values into the formula:
[tex]\[ F = (1.7 \times 10^3 \text{ kg}) \cdot (4.75 \text{ m/s}^2) \][/tex]
Calculating this product:
[tex]\[ F = 1.7 \times 10^3 \times 4.75 \][/tex]
[tex]\[ F = 1.7 \times 4.75 \times 10^3 \][/tex]
[tex]\[ F = 8.075 \times 10^3 \][/tex]
Therefore, the magnitude of the force is:
[tex]\[ F = 8075 \text{ newtons} \][/tex]
Comparing this value with the options provided:
- A. \( 3.6 \times 10^2 \) newtons
- B. \( 1.7 \times 10^3 \) newtons
- C. \( 8.1 \times 10^3 \) newtons
- D. \( 9.0 \times 10^3 \) newtons
The option closest to our calculated force of 8075 newtons is:
[tex]\[ C. 8.1 \times 10^3 \text{ newtons} \][/tex]
Thus, the correct answer is:
[tex]\[ C. 8.1 \times 10^3 \text{ newtons} \][/tex]
