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What force is needed to accelerate a truck with a mass of [tex]3,000 \, \text{kg}[/tex] at a rate of [tex]2.0 \, \text{m/s}^2[/tex]?

A. [tex]3000 \, \text{N}[/tex]
B. [tex]1500 \, \text{N}[/tex]
C. [tex]12,000 \, \text{N}[/tex]
D. [tex]6000 \, \text{N}[/tex]

Sagot :

GinnyAnswer
To determine the force needed to accelerate a truck with a given mass, we use Newton's Second Law of Motion. This law states that the force [tex]\( F \)[/tex] acting on an object is equal to the mass [tex]\( m \)[/tex] of the object multiplied by the acceleration [tex]\( a \)[/tex] of the object. The formula is given by:

[tex]\[ F = m \cdot a \][/tex]

Here's the step-by-step process:

1. Identify the given values:
- Mass ([tex]\( m \)[/tex]) of the truck: 3000 kg
- Acceleration ([tex]\( a \)[/tex]): 2.0 m/s²

2. Substitute the given values into the formula:
[tex]\[ F = 3000 \, \text{kg} \times 2.0 \, \text{m/s}^2 \][/tex]

3. Perform the multiplication:
[tex]\[ F = 6000 \, \text{N} \][/tex]

4. Interpret the result:
The calculated force [tex]\( F \)[/tex] needed to accelerate the truck is 6000 N.

So, the correct answer is:
[tex]\[ D. \ 6000 \ \text{N} \][/tex]
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