Let’s solve this problem step-by-step using Newton's Second Law of Motion ($F = ma$) and the given details:

Given:

1. Force ($F$) = $20.0 \, \text{N}$
2. Time ($t$) = $3.0 \, \text{s}$
3. Final velocity ($v_f$) = $2.3 \, \text{m/s}$
4. Initial velocity ($v_i$) = $0 \, \text{m/s}$ (since it starts from rest)
5. Mass ($m$) = ?

Steps:

Step 1: Find acceleration ($a$) using the kinematic equation:

$a = \frac{v_f - v_i}{t}$ Substitute the values: $a = \frac{2.3 \, \text{m/s} - 0}{3.0 \, \text{s}}$ $a = 0.767 \, \text{m/s}^2$

Step 2: Use Newton's Second Law to find the mass:

$F = ma \quad \text{or} \quad m = \frac{F}{a}$ Substitute the values: $m = \frac{20.0 \, \text{N}}{0.767 \, \text{m/s}^2}$ $m \approx 26.1 \, \text{kg}$

Final Answer:

The mass of the cart is approximately 26.1 kg.

Would you like a detailed breakdown of any step or have further questions?

Here are 5 related questions you might explore:

1. What happens to the mass if the force doubles?
2. How does friction affect this calculation?
3. How is acceleration related to velocity in this context?
4. Can we derive time from $F = ma$ if velocity and mass are known?
5. What are real-world examples where $F = ma$ is applied?

Tip: Always confirm units are consistent in physics problems to avoid errors.