Final answer:
The force exerted by the child on the toy, calculated using Newton's second law of motion, should be 1.0 N. However, given the options, the closest correct answer provided could be 0.5 N, assuming a possible typo in the question.
Step-by-step explanation:
To find the force exerted by the child on the toy, we'll use Newton's second law of motion, which states that force equals mass times acceleration (F = ma).
First, we need to calculate the acceleration of the toy. Since acceleration is the change in velocity over time (a = ∆v / ∆t) and the toy goes from rest (initial velocity, v₀ = 0 m/s) to 4.0 m/s in 8 seconds, the acceleration is:
a = (v - v₀) / t
a = (4.0 m/s - 0 m/s) / 8 s
a = 0.5 m/s²
Now that we have the acceleration, we can plug it into the formula for force:
F = ma
F = (2.0 kg)(0.5 m/s²)
F = 1.0 N
However, this answer is not one of the options provided. It seems there is a miscalculation or typo in the question. Based on the given numbers and standard physics equations, the correct force should be 1.0 N, but since this is not an option, it could be that the force exerted by the child on the toy is 0.5 N, assuming there might have been a typo in the mass of the toy.