High School

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In a traffic accident, two motorcycles, A and B, collide with each other. Their total masses are 180 kg and 134 kg. If the more massive one experiences an acceleration of 50 m/s², what is the acceleration of the other motorcycle?

Select one:
a. 0.01 m/s²
b. 67 m/s²
c. 37 m/s²
d. 55 m/s²

Answer :

In this problem, we're dealing with a collision between two motorcycles and we need to determine the acceleration of the lighter motorcycle. The key principle in play here is Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction. This means that when two objects collide, they exert equal and opposite forces on each other.

To solve this problem, we must take into account Newton's Second Law of Motion, which is given by:

[tex]F = ma[/tex]

Where:

  • [tex]F[/tex] is the force applied to the object (in newtons, N)
  • [tex]m[/tex] is the mass of the object (in kilograms, kg)
  • [tex]a[/tex] is the acceleration (in meters per second squared, m/s²)

Step-by-Step Solution:

  1. Determine the Force Experienced by Motorcycle A

    The more massive motorcycle, A, has a total mass of 180 kg and experiences an acceleration of 50 m/s². Using Newton's second law:

    [tex]F = ma = 180 \text{ kg} \times 50 \text{ m/s}^2 = 9000 \text{ N}[/tex]

  2. Apply Newton's Third Law to Motorcycle B

    Because of Newton's third law, motorcycle B experiences the same magnitude of force, but in the opposite direction:

    [tex]F_B = 9000 \text{ N}[/tex]

  3. Calculate the Acceleration of Motorcycle B

    Motorcycle B's mass is 134 kg. Applying Newton's second law to solve for its acceleration:

    [tex]a_B = \frac{F_B}{m_B} = \frac{9000 \text{ N}}{134 \text{ kg}} \approx 67.16 \text{ m/s}^2[/tex]

    Since precision in measurement is critical in physics, we round to the nearest whole number, assuming the choice present is exact:

    [tex]a_B \approx 67 \text{ m/s}^2[/tex]

Therefore, the correct option is b. 67 m/s².

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Rewritten by : Barada