Answer :
To determine the magnitude of force required to accelerate a car with a mass of [tex]\(1.7 \times 10^3\)[/tex] kilograms at an acceleration of [tex]\(4.75\)[/tex] meters per second squared, we can use Newton's second law of motion, which is formulated as:
[tex]\[ F = m \times a \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( a \)[/tex] is the acceleration.
Given:
- [tex]\( m = 1.7 \times 10^3 \)[/tex] kg,
- [tex]\( a = 4.75 \)[/tex] m/s²,
we substitute the values into the formula:
[tex]\[ F = (1.7 \times 10^3 \, \text{kg}) \times 4.75 \, \text{m/s}^2 \][/tex]
By multiplying these values, we find:
[tex]\[ F = 1.7 \times 4.75 \times 10^3 \, \text{N} \][/tex]
[tex]\[ F = 8.075 \times 10^3 \, \text{N} \][/tex]
Therefore, the magnitude of the force required to accelerate the car is [tex]\( 8075.0 \)[/tex] newtons, which corresponds to one of the provided options:
C. [tex]\( 8.1 \times 10^3 \)[/tex] newtons
Thus, the correct answer is:
[tex]\[ \boxed{8.1 \times 10^3 \, \text{newtons}} \][/tex]
[tex]\[ F = m \times a \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( a \)[/tex] is the acceleration.
Given:
- [tex]\( m = 1.7 \times 10^3 \)[/tex] kg,
- [tex]\( a = 4.75 \)[/tex] m/s²,
we substitute the values into the formula:
[tex]\[ F = (1.7 \times 10^3 \, \text{kg}) \times 4.75 \, \text{m/s}^2 \][/tex]
By multiplying these values, we find:
[tex]\[ F = 1.7 \times 4.75 \times 10^3 \, \text{N} \][/tex]
[tex]\[ F = 8.075 \times 10^3 \, \text{N} \][/tex]
Therefore, the magnitude of the force required to accelerate the car is [tex]\( 8075.0 \)[/tex] newtons, which corresponds to one of the provided options:
C. [tex]\( 8.1 \times 10^3 \)[/tex] newtons
Thus, the correct answer is:
[tex]\[ \boxed{8.1 \times 10^3 \, \text{newtons}} \][/tex]
