SOLUTION: A cat walks in a straight line, which we shall call the x-axis, with the positive direction to the right. As an observant physicist, you make measurements of this cat's motion and

Question 1204892: A cat walks in a straight line, which we shall call the x-axis, with the positive direction to the right. As an observant physicist, you make measurements of this cat's motion and construct a graph of the feline's velocity as a function of time (Fig. E2.26). (link for the Fig. E2.26: https://i.postimg.cc/fRgY00DK/Figure-E2-26.png )
(a) Find the cat's velocity at t = 4.0s and at t = 7.0s.
(b) What is the cat's acceleration at t = 3.0s? At t = 6.0s? At t = 7.0s?
(c) What distance does the cat move during the first 4.5s? From t = 0 to t = 7.0s?
(d) Assuming that the cat started at the origin, sketch clear graphs of the cat's acceleration and position as functions of time.
Answer by textot(100) (Show Source): You can put this solution on YOUR website!
**a) Find the cat's velocity at t = 4.0s and at t = 7.0s.**
* **At t = 4.0s:**
* Read the value of the velocity from the graph at t = 4.0s. Let's assume the graph shows the velocity at t = 4.0s is **v(4.0s) = 2 m/s** (You'll need to read the actual value from the graph).
* **At t = 7.0s:**
* Read the value of the velocity from the graph at t = 7.0s. Let's assume the graph shows the velocity at t = 7.0s is **v(7.0s) = -1 m/s** (You'll need to read the actual value from the graph).
**b) What is the cat's acceleration at t = 3.0s? At t = 6.0s? At t = 7.0s?**
* **Acceleration is the slope of the velocity-time graph.**
* **At t = 3.0s:**
* Determine the slope of the velocity-time graph at t = 3.0s. If the graph is linear around this point, the acceleration is constant.
* Let's assume the slope at t = 3.0s is **a(3.0s) = 1 m/s²** (You'll need to calculate the slope from the graph).
* **At t = 6.0s:**
* Determine the slope of the velocity-time graph at t = 6.0s.
* Let's assume the slope at t = 6.0s is **a(6.0s) = -2 m/s²** (You'll need to calculate the slope from the graph).
* **At t = 7.0s:**
* Determine the slope of the velocity-time graph at t = 7.0s.
* Let's assume the slope at t = 7.0s is **a(7.0s) = 0 m/s²** (You'll need to calculate the slope from the graph).
**c) What distance does the cat move during the first 4.5s? From t = 0 to t = 7.0s?**
* **Distance is represented by the area under the velocity-time graph.**
* **Distance during the first 4.5s:**
* Calculate the area under the velocity-time graph from t = 0s to t = 4.5s.
* This might involve calculating the areas of triangles, rectangles, or other shapes depending on the shape of the graph.
* Let's assume the distance traveled during the first 4.5s is **10 meters** (You'll need to calculate the area from the graph).
* **Distance from t = 0 to t = 7.0s:**
* Calculate the total area under the velocity-time graph from t = 0s to t = 7.0s.
* This might involve calculating the areas of triangles, rectangles, or other shapes depending on the shape of the graph.
* Let's assume the total distance traveled is **12 meters** (You'll need to calculate the area from the graph).
**d) Sketch clear graphs of the cat's acceleration and position as functions of time.**
* **Acceleration vs. Time:**
* Plot the acceleration values you found in part (b) at the corresponding times.
* Connect the points to create the acceleration-time graph. This graph will likely have segments with constant acceleration (horizontal lines) and segments where the acceleration changes (sloped lines).
* **Position vs. Time:**
* Since the cat's initial position is at the origin, the position-time graph will start at (0,0).
* The slope of the position-time graph at any point is equal to the velocity at that time.
* Use the velocity-time graph to determine the slopes at different times and sketch the corresponding position-time graph. This graph will likely be curved since the velocity is not constant.
**Important Notes:**
* **Read the Graph Carefully:** The accuracy of your answers depends entirely on your ability to accurately read the values from the provided velocity-time graph (Fig. E2.26).
* **Units:** Always include units in your answers (e.g., m/s for velocity, m/s² for acceleration, meters for distance, seconds for time).
* **Graphing:** Use graph paper or graphing software to create accurate and clear graphs of acceleration and position.
This analysis provides a general framework for solving this problem. You'll need to use the specific information and values from the provided graph (Fig. E2.26) to obtain the correct numerical answers.

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