A particle starts at x=0.00 meters. The object moves to a position of x=5.0 meters. It then moves to a position of  -3.2 meters. It then moves to 8.0 meters. The overall time it takes to complete the motion is 0.444 minutes. Determine the speed of the particle 

To determine the **speed** of the particle, we need to calculate the **total distance** traveled and then divide it by the **total time**.

### Step 1: Calculate the total distance traveled
The particle's motion involves several steps:
1. From \( x = 0.0 \) meters to \( x = 5.0 \) meters:
   \[
   \text{Distance} = 5.0 - 0.0 = 5.0 \, \text{meters}
   \]
2. From \( x = 5.0 \) meters to \( x = -3.2 \) meters:
   \[
   \text{Distance} = |5.0 - (-3.2)| = 5.0 + 3.2 = 8.2 \, \text{meters}
   \]
3. From \( x = -3.2 \) meters to \( x = 8.0 \) meters:
   \[
   \text{Distance} = |8.0 - (-3.2)| = 8.0 + 3.2 = 11.2 \, \text{meters}
   \]

Now, sum the distances:
\[
\text{Total distance} = 5.0 + 8.2 + 11.2 = 24.4 \, \text{meters}
\]

### Step 2: Convert the total time into seconds
The total time is given as \( 0.444 \, \text{minutes} \). Since there are 60 seconds in a minute:
\[
\text{Total time} = 0.444 \times 60 = 26.64 \, \text{seconds}
\]

### Step 3: Calculate the speed
The speed is the total distance traveled divided by the total time:
\[
\text{Speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{24.4 \, \text{meters}}{26.64 \, \text{seconds}} \approx 0.916 \, \text{m/s}
\]

### Final Answer:
The speed of the particle is approximately \( 0.916 \, \text{m/s} \).

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Would you like more details or have any questions about this? Here are some related questions:

1. What is the difference between speed and velocity?
2. How does displacement differ from total distance traveled?
3. Can the average velocity of the particle be calculated?
4. What would the speed be if the time were reduced by half?
5. How does acceleration factor into this problem?

**Tip:** Speed is a scalar quantity—it only considers magnitude, while velocity includes both magnitude and direction.

A particle starts at x=0.00 meters. The object moves to a position of x=5.0 meters. It then moves to a position of -3.2 meters. It then moves to 8.0 meters. The overall time it takes to complete the motion is 0.444 minutes. Determine the speed of the particle.

This problem involves calculating the speed of a particle moving through several positions from x=0.0 meters to x=5.0 meters, then to -3.2 meters, and finally to 8.0 meters in a total time of 0.444 minutes. The solution includes key kinematic concepts like distance and speed, unit conversion, and the scalar nature of speed. Suitable for students in Grades 9-10.

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