To determine the force needed, we can use Newton's second law, which states that force (F) is equal to mass (m) multiplied by acceleration (a).

Given:

Mass of the wagon, m = 6 kg

Initial speed, u = 0 m/s (since it starts from rest)

Final speed, v = 10 m/s

Time taken, t = 5 seconds

First, we need to calculate acceleration (a) using the formula:

a = (v - u) / t

Substituting values:

a = (10 - 0) / 5

a = 2 m/s²

Now, we can calculate the force (F) using the formula:

F = m * a

Substituting values:

F = 6 kg * 2 m/s²

F = 12 N

Therefore, a force of 12 Newtons is needed to accelerate the 6 kg wagon from rest to a speed of 10 m per second in 5 seconds.