The graph below tracks the movement of a vehicle over a period of time, starting from position x = 0 km at time t = 0 hr Based on the graph, what is the vehicle’s velocity, to the nearest 0.1 km/hr if the labeled point has coordinates (4,35)?

To find the vehicle's velocity based on the graph, we need to calculate the slope of the line between the points given on the graph. The slope represents the velocity, as it is the change in position (distance) over the change in time.

The slope formula is:

\[
\text{Velocity} = \frac{\Delta x}{\Delta t}
\]

Where:
- \(\Delta x\) is the change in position (in kilometers),
- \(\Delta t\) is the change in time (in hours).

Given:
- The point \((t_1, x_1)\) is \((0, 0)\), since the vehicle starts at position \(x = 0\) km at time \(t = 0\) hr.
- The point \((t_2, x_2)\) is \((4, 35)\), meaning the vehicle is at 35 km at time 4 hours.

Now, calculate the velocity:

\[
\text{Velocity} = \frac{35 \, \text{km} - 0 \, \text{km}}{4 \, \text{hr} - 0 \, \text{hr}} = \frac{35 \, \text{km}}{4 \, \text{hr}} = 8.75 \, \text{km/hr}
\]

So, the vehicle's velocity is **8.8 km/hr** to the nearest 0.1 km/hr.

Would you like further explanation, or do you have any other questions? Here are some related questions:

1. What would be the velocity if the vehicle traveled 50 km in the same time?
2. How would the velocity change if the time taken was halved?
3. What is the average speed of the vehicle if it returns to the starting point after another 4 hours?
4. How far would the vehicle travel in 6 hours at this velocity?
5. What is the significance of the slope of a position-time graph?

**Tip:** Remember that the slope of a position vs. time graph directly represents the object's velocity.

Learn how to calculate the velocity of a vehicle from a position-time graph. This math problem involves finding the slope between two points on the graph to determine velocity. Explore step-by-step solution and related questions. Suitable for high school students.

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