https://file.aiquickdraw.com/mathbot/file/1726392173605awom9o0v.jpg

Let's analyze the problem based on the provided graph and tasks.

### The key points and tasks (translated):
- You need to derive information from the graph based on the relationship between position (paikka) and time (aika).
- The formula for speed (nopeus) is given as:
  \[
  \text{Nopeus} = \frac{\Delta \text{paikka}}{\Delta \text{aika}} = \frac{\Delta s}{\Delta t}
  \]
  (change in position / change in time).
- Acceleration (kiihtyvyys) is given as:
  \[
  \text{Kiihtyvyys} = \frac{\Delta \text{nopeus}}{\Delta \text{aika}} = \frac{\Delta v}{\Delta t}
  \]
  (change in speed / change in time).

Let's go through the specific parts:

### a) Position at 5 ms (paikka hetkellä 5 ms)
From the graph, at **5 ms**, it appears the position is about **1.5 cm**.

### b) Speed between 0 ms and 4 ms (nopeus aikavälillä 0 ms - 4 ms)
To calculate speed:
- At **0 ms**, the position is **1.0 cm**.
- At **4 ms**, the position is **1.4 cm**.
Using the speed formula:
\[
v = \frac{\Delta s}{\Delta t} = \frac{1.4 \, \text{cm} - 1.0 \, \text{cm}}{4 \, \text{ms} - 0 \, \text{ms}} = \frac{0.4}{4} = 0.1 \, \text{cm/ms}
\]

### c) Speed between 6 ms and 8 ms (nopeus aikavälillä 6 ms - 8 ms)
- At **6 ms**, the position is **1.6 cm**.
- At **8 ms**, the position is **1.8 cm**.
Using the same formula:
\[
v = \frac{1.8 \, \text{cm} - 1.6 \, \text{cm}}{8 \, \text{ms} - 6 \, \text{ms}} = \frac{0.2}{2} = 0.1 \, \text{cm/ms}
\]

### d) Slope from the graph (kulmakerroin)
The slope from the graph can be calculated as the change in position over the change in time. From the example above, the slope appears to be around **0.1 cm/ms**, as shown in parts (b) and (c).

### e) Convert the slope to SI units (muunna kulmakerroin SI-yksiköihin)
Since the current units are in **cm/ms**, and the SI unit for speed is **m/s**:
\[
1 \, \text{cm/ms} = 10 \, \text{m/s}
\]
So, the slope in SI units would be:
\[
0.1 \, \text{cm/ms} = 1 \, \text{m/s}
\]

### f) Acceleration at 10 ms (kiihtyvyys hetkellä 10 ms)
At **10 ms**, the graph shows no significant change in speed, which suggests the acceleration is zero:
\[
a = 0 \, \text{m/s}^2
\]

Would you like any further clarifications or more detailed explanations?

### 5 Related Questions:
1. How do you calculate the slope of a line graph in general?
2. What is the difference between speed and velocity?
3. Can you explain how to derive acceleration from a position vs. time graph?
4. How does uniform motion differ from accelerated motion?
5. How are non-SI units converted to SI units in physics?

**Tip**: Always ensure the units are consistent when calculating physical quantities, especially when converting to or from SI units.

Selvitä alla olevasta kuvaajasta, kun nopeus = paikan muutos / ajan muutos ja kiihtyvyys = nopeuden muutos / ajan muutos. Paikka ajan funktiona.

Learn how to determine speed and acceleration from a position-time graph using basic kinematic equations. This problem involves calculating position at specific times, determining speed between time intervals, and converting slope to SI units. Suitable for high school physics students.

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