Question
blessing was chased by a dog after walking past it. she was initially walking at a constant speed of 3m/s. If she Increases her speed at the rate of 3.5m/s² for 4 secs until the dog stopped she maintained the attained speed until she got to the junction of her house 15 secs after. Afterwards, she decelerated home to rest for 5 secs. Plot the velocity time graph from the moment the dog started chasing her.
Answers
GPT-4o mini
To plot the velocity-time graph for Blessing's scenario, we will break down her movements into phases based on her speed during those intervals.
### Phase 1: Acceleration
- **Initial speed, \( v_0 = 3 \, \text{m/s} \)**
- **Acceleration, \( a = 3.5 \, \text{m/s}^2 \)**
- **Time interval, \( t = 4 \, \text{s} \)**
We calculate her final velocity after 4 seconds of acceleration using the formula:
\[
v = v_0 + a t
\]
Substituting in the values:
\[
v = 3 \, \text{m/s} + (3.5 \, \text{m/s}^2 \times 4 \, \text{s}) = 3 \, \text{m/s} + 14 \, \text{m/s} = 17 \, \text{m/s}
\]
### Phase 2: Constant Speed
- After accelerating for 4 seconds, she maintains a constant speed of \( 17 \, \text{m/s} \).
- **Time interval, \( t = 15 \, \text{s} \)** (15 seconds total, but after 4 seconds of acceleration, hence she travels at this speed for 11 seconds).
### Phase 3: Deceleration
- After 15 seconds (4 seconds of acceleration + 11 seconds of constant speed), she begins deceleration.
- For simplicity, let's assume that this portion lasts for \( t = 5 \, \text{s} \).
- We need to define how much she decelerates and at what rate. If absolute deceleration information is not provided, we'll assume a simple case where she comes to rest over 5 seconds (final speed = 0 m/s).
For this deceleration:
\[
\text{Initial speed before deceleration} = 17 \, \text{m/s}
\]
Assuming uniform deceleration:
Let \( a_d \) be the deceleration rate. Using the formula:
\[
v_f = v_i + a_d t
\]
Setting \( v_f = 0 \, \text{m/s} \):
\[
0 = 17 \, \text{m/s} + a_d \times 5 \, \text{s}
\]
Solving for \( a_d \):
\[
a_d = -\frac{17 \, \text{m/s}}{5 \, \text{s}} = -3.4 \, \text{m/s}^2
\]
### Summary of Velocity at Each Interval:
- **0 to 4 seconds**: Accelerates from \( 3 \, \text{m/s} \) to \( 17 \, \text{m/s} \)
- **4 to 15 seconds**: Constant speed at \( 17 \, \text{m/s} \)
- **15 to 20 seconds**: Decelerates from \( 17 \, \text{m/s} \) to \( 0 \, \text{m/s} \)
### Plotting the Graph
Now we can plot the velocity-time graph based on this analysis.
1. Start at (0, 3)
2. At (4, 17) - velocity increases to 17 m/s
3. From (4, 17) to (15, 17) - constant velocity
4. End at (20, 0) - decrease to 0 m/s
The points to plot are:
- (0, 3)
- (4, 17)
- (15, 17)
- (20, 0)
Connect the points with straight lines corresponding to each phase.
### Sketch of the Graph
- On the x-axis, label time from 0 to 20 seconds.
- On the y-axis, label velocity from 0 to about 18 m/s.
- Plot the points and connect them as per the phases mentioned.
This graph visually represents Blessing's velocity over time as she reacts to the dog chasing her.
### Phase 1: Acceleration
- **Initial speed, \( v_0 = 3 \, \text{m/s} \)**
- **Acceleration, \( a = 3.5 \, \text{m/s}^2 \)**
- **Time interval, \( t = 4 \, \text{s} \)**
We calculate her final velocity after 4 seconds of acceleration using the formula:
\[
v = v_0 + a t
\]
Substituting in the values:
\[
v = 3 \, \text{m/s} + (3.5 \, \text{m/s}^2 \times 4 \, \text{s}) = 3 \, \text{m/s} + 14 \, \text{m/s} = 17 \, \text{m/s}
\]
### Phase 2: Constant Speed
- After accelerating for 4 seconds, she maintains a constant speed of \( 17 \, \text{m/s} \).
- **Time interval, \( t = 15 \, \text{s} \)** (15 seconds total, but after 4 seconds of acceleration, hence she travels at this speed for 11 seconds).
### Phase 3: Deceleration
- After 15 seconds (4 seconds of acceleration + 11 seconds of constant speed), she begins deceleration.
- For simplicity, let's assume that this portion lasts for \( t = 5 \, \text{s} \).
- We need to define how much she decelerates and at what rate. If absolute deceleration information is not provided, we'll assume a simple case where she comes to rest over 5 seconds (final speed = 0 m/s).
For this deceleration:
\[
\text{Initial speed before deceleration} = 17 \, \text{m/s}
\]
Assuming uniform deceleration:
Let \( a_d \) be the deceleration rate. Using the formula:
\[
v_f = v_i + a_d t
\]
Setting \( v_f = 0 \, \text{m/s} \):
\[
0 = 17 \, \text{m/s} + a_d \times 5 \, \text{s}
\]
Solving for \( a_d \):
\[
a_d = -\frac{17 \, \text{m/s}}{5 \, \text{s}} = -3.4 \, \text{m/s}^2
\]
### Summary of Velocity at Each Interval:
- **0 to 4 seconds**: Accelerates from \( 3 \, \text{m/s} \) to \( 17 \, \text{m/s} \)
- **4 to 15 seconds**: Constant speed at \( 17 \, \text{m/s} \)
- **15 to 20 seconds**: Decelerates from \( 17 \, \text{m/s} \) to \( 0 \, \text{m/s} \)
### Plotting the Graph
Now we can plot the velocity-time graph based on this analysis.
1. Start at (0, 3)
2. At (4, 17) - velocity increases to 17 m/s
3. From (4, 17) to (15, 17) - constant velocity
4. End at (20, 0) - decrease to 0 m/s
The points to plot are:
- (0, 3)
- (4, 17)
- (15, 17)
- (20, 0)
Connect the points with straight lines corresponding to each phase.
### Sketch of the Graph
- On the x-axis, label time from 0 to 20 seconds.
- On the y-axis, label velocity from 0 to about 18 m/s.
- Plot the points and connect them as per the phases mentioned.
This graph visually represents Blessing's velocity over time as she reacts to the dog chasing her.
show me the graph
GPT-4o mini
I cannot create visual graphics directly in this text-based format, but I can help you visualize how to draw the graph based on the provided information.
### Steps to Draw the Velocity-Time Graph:
1. **Set Up Your Axes:**
- **X-axis (Time):** Label it from 0 to 20 seconds.
- **Y-axis (Velocity):** Label it from 0 to 18 m/s (you can go a bit above to give some space).
2. **Plotting the Points:**
- Point A (0, 3): Start at the point where time is 0 seconds and velocity is 3 m/s.
- Point B (4, 17): From (0, 3), draw a straight line up to (4, 17). This is where she finishes accelerating.
- Point C (15, 17): From (4, 17), draw a horizontal line to (15, 17). This represents the constant speed.
- Point D (20, 0): From (15, 17), draw a straight line down to (20, 0). This shows her coming to a stop.
3. **Connecting the Dots:**
- Connect Point A to Point B with a straight line (this represents acceleration).
- Draw a horizontal line from Point B to Point C.
- Finally, connect Point C to Point D with a straight line (representing deceleration).
### Description of the Graph:
- **From 0 to 4 seconds:** The line slopes upwards, indicating a rise in velocity from 3 m/s to 17 m/s.
- **From 4 to 15 seconds:** The horizontal line shows constant velocity at 17 m/s.
- **From 15 to 20 seconds:** The line slopes downwards, indicating a decrease in velocity from 17 m/s to 0 m/s.
### Using Graphing Software:
If you want to create a more precise graph, you could use tools like:
- Microsoft Excel
- Google Sheets
- Desmos (Online Graphing Calculator)
- Any graph paper
Simply input the points as coordinates and follow the steps to connect them appropriately.
If you are still having trouble visualizing it or if you want, I can guide you through the steps of using one of these software tools to create it!
### Steps to Draw the Velocity-Time Graph:
1. **Set Up Your Axes:**
- **X-axis (Time):** Label it from 0 to 20 seconds.
- **Y-axis (Velocity):** Label it from 0 to 18 m/s (you can go a bit above to give some space).
2. **Plotting the Points:**
- Point A (0, 3): Start at the point where time is 0 seconds and velocity is 3 m/s.
- Point B (4, 17): From (0, 3), draw a straight line up to (4, 17). This is where she finishes accelerating.
- Point C (15, 17): From (4, 17), draw a horizontal line to (15, 17). This represents the constant speed.
- Point D (20, 0): From (15, 17), draw a straight line down to (20, 0). This shows her coming to a stop.
3. **Connecting the Dots:**
- Connect Point A to Point B with a straight line (this represents acceleration).
- Draw a horizontal line from Point B to Point C.
- Finally, connect Point C to Point D with a straight line (representing deceleration).
### Description of the Graph:
- **From 0 to 4 seconds:** The line slopes upwards, indicating a rise in velocity from 3 m/s to 17 m/s.
- **From 4 to 15 seconds:** The horizontal line shows constant velocity at 17 m/s.
- **From 15 to 20 seconds:** The line slopes downwards, indicating a decrease in velocity from 17 m/s to 0 m/s.
### Using Graphing Software:
If you want to create a more precise graph, you could use tools like:
- Microsoft Excel
- Google Sheets
- Desmos (Online Graphing Calculator)
- Any graph paper
Simply input the points as coordinates and follow the steps to connect them appropriately.
If you are still having trouble visualizing it or if you want, I can guide you through the steps of using one of these software tools to create it!