Final answer:
The expression for the child's speed, v, is found using the momentum formula P = m * v, and by rearranging it to v = P / m. With the given momentum P of 666 kg*m/s and mass m of 12 kg, the child's speed is calculated as v = 55.5 m/s.
Step-by-step explanation:
To find the child's speed, v, when they are riding a bicycle with a combined mass, m, of 12 kg and a linear momentum of magnitude P of 666 kg∙m/s, we can use the formula for linear momentum, P = m ∙ v, where P is the momentum, m is the mass, and v is the velocity. Solving for v, we get v = P / m.
Substituting the given values, we find that v = 666 kg∙m/s / 12 kg, which simplifies to v = 55.5 m/s. Thus, the expression for the child's speed is v = P / m.