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.

Answer 1

show me the graph

Answer 2

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.

Answer 3

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!