Answered

Select the correct answer.

What is the magnitude of force required to accelerate a car of mass [tex]$1.7 \times 10^3$[/tex] kilograms by [tex]4.75 \, \text{meters/second}^2[/tex]?

A. [tex]$3.6 \times 10^2$[/tex] newtons
B. [tex][tex]$1.7 \times 10^3$[/tex][/tex] newtons
C. [tex]$8.1 \times 10^3$[/tex] newtons
D. [tex]$9.0 \times 10^3$[/tex] newtons



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]