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Natali5045456 [20]
2 years ago
9

Z. A force that gives a 8-kg objet an acceleration of 1.6 m/s^2 would give a 2-kg object an

Physics
1 answer:
Paladinen [302]2 years ago
4 0

Answer:

\boxed {\boxed {\sf D.\ 6.4\ m/s^2}}

Explanation:

We need to find the acceleration of the 2 kilogram object. Let's complete this in 2 steps.

<h3>1. Force of 1st Object </h3>

First, we can find the force of the first, 8 kilogram object.

According to Newton's Second Law of Motion, force is the product of mass and acceleration.

F=m \times a

The mass of the object is 8 kilograms and the acceleration is 1.6 meters per square second.

  • m= 8 kg
  • a= 1.6 m/s²

Substitute these values into the formula.

F= 8 \ kg * 1.6 \ m/s^2

Multiply.

F= 12.8 \ kg*m/s^2

<h3>2. Acceleration of the 2nd Object </h3>

Now,  use the force we just calculated to complete the second part of the problem. We use the same formula:

F= m \times a

This time, we know the force is 12.8 kilograms meters per square second and the mass is 2 kilograms.

  • F= 12.8 kg *m/s²
  • m= 2 kg

Substitute the values into the formula.

12.8 \ kg*m/s^2= 2 \ kg *a

Since we are solving for the acceleration, we must isolate the variable (a). It is being multiplied by 2 kg. The inverse of multiplication is division. Divide both sides of the equation by 2 kg.

\frac {12.8 \ kg*m/s^2}{2 \ kg}= \frac{2\ kg* a}{2 \ kg}

\frac {12.8 \ kg*m/s^2}{2 \ kg}=a

The units of kilograms cancel.

\frac {12.8}{2}\ m/s^2=a

6.4 \ m/s^2=a

The acceleration is 6.4 meters per square second.

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