https://file.aiquickdraw.com/mathbot/file/172558896092489hpamc2.jpg

What is the bicyclist's velocity at  t=10s ?

To determine the bicyclist's velocity at \( t = 10 \) seconds from the given position-time graph, we need to calculate the slope of the graph at \( t = 10 \) seconds.

### Steps:
1. Identify the segment of the graph where \( t = 10 \) seconds lies. 
2. Determine the slope (velocity) of that segment.

From the graph:
- Between \( t = 0 \) and \( t = 20 \) seconds, the position \( x(t) \) increases linearly from 50 m to 100 m.
  
Since \( t = 10 \) seconds falls within this linear segment, the velocity (which is the slope of the line) can be calculated as follows:

\[
\text{Velocity} = \frac{\Delta x}{\Delta t} = \frac{100\,\text{m} - 50\,\text{m}}{20\,\text{s} - 0\,\text{s}} = \frac{50\,\text{m}}{20\,\text{s}} = 2.5\,\text{m/s}
\]

### Conclusion:
The velocity of the bicyclist at \( t = 10 \) seconds is \( 2.5 \, \text{m/s} \).

Do you have any questions or need more details on this? Here are 5 related questions you might find helpful:

1. What is the bicyclist's velocity at \( t = 25 \) seconds?
2. How would you find the average velocity over the entire time interval?
3. What is the velocity at \( t = 35 \) seconds?
4. Can you determine the acceleration of the bicyclist during the first 20 seconds?
5. How would you describe the motion of the bicyclist between \( t = 30 \) and \( t = 40 \) seconds?

**Tip**: The slope of a position-time graph gives you the velocity, so always look for straight-line segments to easily calculate constant velocities.

What is the bicyclist's velocity at t=10s?

Learn how to calculate the velocity of a bicyclist at t=10s from a position-time graph. The problem involves key concepts from kinematics, including the use of the slope of a graph to determine velocity. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation