In a collision between two motorcycles, if motorcycle A has a mass of 180 kg and accelerates at 50 m/s², what is the acceleration of motorcycle B, which has a mass of 134 kg?

To understand why the acceleration of motorcycle B is calculated to be approximately 67 m/s², we can apply Newton's second law of motion, which states that force equals mass times acceleration (F = ma).

In the context of the collision, the force exerted on each motorcycle can be analyzed. Motorcycle A is accelerating at 50 m/s² and has a mass of 180 kg. Therefore, the total force exerted by motorcycle A can be determined using the equation:

[

F_A = m_A \cdot a_A = 180 , \text{kg} \cdot 50 , \text{m/s}² = 9000 , \text{N}.

]

In a collision, the forces involved must be equal and opposite due to Newton's third law of motion. Thus, motorcycle B will experience the same magnitude of force acting on it, but in the opposite direction. Given that we want to find the acceleration of motorcycle B, we rearrange the formula for force to solve for acceleration:

[

a_B = \frac{F_B}{m_B}.

]

Since motorcycle B experiences the same force as motorcycle A, we set (F_B) equal to