The only force acting on a 1.5 kg body as it moves along the axis varies as shown below. The scale of the figure's vertical axis is set by F = 4.4 N. The velocity of the body at x = 0 is 4.1 m/s. Fx (N) KED 1 2 3 4 5 F 0 x (m) (a) What is the kinetic energy of the body at x = 3.0 m? -4.4 X J

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### Force Acting on a Body

The only force acting on a 1.5 kg body as it moves along the \( x \)-axis varies as shown below. The scale of the figure's vertical axis is set by \( F_s = 4.4 \) N. The velocity of the body at \( x = 0 \) is 4.1 m/s.

#### Force vs. Displacement Graph

The graph below shows the relationship between the force \( F_x \) (in Newtons) and the displacement \( x \) (in meters).

- **X-Axis (Displacement \( x \))**: Ranges from 0 m to 5 m.
- **Y-Axis (Force \( F_x \))**: Ranges from \(-F_s\) to \(F_s\) (\(-4.4 \text{ N}\) to \(4.4 \text{ N}\)).

The force decreases linearly from \( F_s \) (4.4 N) at \( x = 0 \) to 0 at \( x = 1 \) m. It then stays at 0 from \( x = 1 \) m to \( x = 5 \) m.

![Graph]

#### Problem

(a) What is the kinetic energy of the body at \( x = 3.0 \) m?

**Solution:**
\[ K.E. = -4.4 \text{ J} \]

(Note: The provided solution of \(-4.4 \text{ J}\) is indicated to be incorrect.)

---

This educational material is designed to help students understand how force varies with displacement and how it affects the kinetic energy of a moving body.
Transcribed Image Text:### Force Acting on a Body The only force acting on a 1.5 kg body as it moves along the \( x \)-axis varies as shown below. The scale of the figure's vertical axis is set by \( F_s = 4.4 \) N. The velocity of the body at \( x = 0 \) is 4.1 m/s. #### Force vs. Displacement Graph The graph below shows the relationship between the force \( F_x \) (in Newtons) and the displacement \( x \) (in meters). - **X-Axis (Displacement \( x \))**: Ranges from 0 m to 5 m. - **Y-Axis (Force \( F_x \))**: Ranges from \(-F_s\) to \(F_s\) (\(-4.4 \text{ N}\) to \(4.4 \text{ N}\)). The force decreases linearly from \( F_s \) (4.4 N) at \( x = 0 \) to 0 at \( x = 1 \) m. It then stays at 0 from \( x = 1 \) m to \( x = 5 \) m. ![Graph] #### Problem (a) What is the kinetic energy of the body at \( x = 3.0 \) m? **Solution:** \[ K.E. = -4.4 \text{ J} \] (Note: The provided solution of \(-4.4 \text{ J}\) is indicated to be incorrect.) --- This educational material is designed to help students understand how force varies with displacement and how it affects the kinetic energy of a moving body.
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