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Select the correct answer.

What is the magnitude of the 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]$1.7 \times 10^3$[/tex] newtons
C. [tex]$8.1 \times 10^3$[/tex] newtons
D. [tex]$9.0 \times 10^3$[/tex] newtons



Answer :

GinnyAnswer
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]

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