Question

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

acceleration of
a. 0.2 m/s2
b. 0.4 m/s2
c. 1.6 m/s2
d. 6.4 m/s2

Answer 1

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

Step-by-step explanation:

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

1. Force of 1st Object

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 * 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`

2. Acceleration of the 2nd Object

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

`F= m * 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}= (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.