Final answer:
The student's question about the final speed and acceleration of a wagon being pushed on a frictionless surface can be solved using the work-energy theorem and Newton's second law. The work done transforms into kinetic energy, allowing the calculation of the final speed, and Newton's second law is applied to find the acceleration. The provided options do not match the correct results from the calculations.
Step-by-step explanation:
The student inquires about the final speed and acceleration of a little red wagon after being pushed by a force on a frictionless surface. To solve this, we can apply the work-energy principle and Newton's second law.
Using the work-energy theorem, work done (W) is equal to the change in kinetic energy. So we have:
W = ∆KE = ½ m(v_f^2 - v_i^2)
Where m is the mass of the wagon, v_i is the initial speed, and v_f is the final speed. The work done by the force is the force times the distance (F × d), so:
W = F × d = 10 N × 3 m = 30 J
Then, we calculate the final speed:
30 J = ½ × 7 kg × (v_f^2 - 4^2)
This results in:
v_f^2 = 4^2 + × (30 J) / (½ × 7 kg)
Solving for v_f gives us the final speed of the wagon.
For acceleration (a), we use Newton's second law (F = m × a), and with the given force (10 N) and mass (7 kg), we can find:
a = F / m = 10 N / 7 kg
This gives us the acceleration produced by the force.
From these calculations, neither of the provided options (a, b, c, d) match the correct results.