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.

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

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RI SƠ 4 years 2021-08-09T11:07:18+00:00 1 Answers 26 views 0

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  1. phucdien
    0
    2021-08-09T11:09:14+00:00
    Reply

    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.

    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 \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

    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 \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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