name: david date: hour:
functions - 8.f.5 hw9
answer the following questions:
1) what does it mean when a graph of speed starts at (0, 0)?
2) if distance is represent on the y - axis and time on the x - axis, what does a line with an upward slope represent?
3) if speed is on the y axis and time on the x - axis, what does a line with a slope of zero represent?
write a short story for the following graphs:
4) graph with speed on y - axis and time on x - axis: starts at (0,0), increases, plateaus, decreases, then plateaus
5) graph with distance from home on y - axis and time on x - axis: starts at a non - zero y - value, plateaus, decreases, plateaus, then decreases to zero

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Accepted Answer

### Question 1
# Brief Explanations:
When a speed - time graph starts at $(0,0)$, it means that at time $t = 0$ (the start of the observation), the speed of the object is $0$. In other words, the object is at rest initially, or its initial speed is zero.
# Answer:
It means the object has an initial speed of 0 (is at rest initially).

### Question 2
# Brief Explanations:
We know that the slope of a line in a distance - time graph ($y$ - axis: distance, $x$ - axis: time) is given by the formula $m=\frac{\Delta y}{\Delta x}=\frac{\text{change in distance}}{\text{change in time}}$. And the formula for speed is $v = \frac{d}{t}$ (where $d$ is distance and $t$ is time). So the slope of the distance - time graph represents speed. An upward - sloping line means that as time ($x$ - axis) increases, the distance ($y$ - axis) also increases. Since slope is speed, an upward slope means the object is moving with a positive speed, i.e., the object is moving away from the starting point (or its position is changing in a positive direction) and its speed is non - zero (because the slope is non - zero and positive). In simpler terms, it represents that the object is moving and its distance from the origin (or starting point) is increasing over time, which implies the object is in motion with a constant or changing (if the slope is changing) speed (but in the case of a straight line, it's constant speed).
# Answer:
An upward - sloping line in a distance - time graph represents that the object is moving (has a non - zero speed) and the distance it travels is increasing as time passes (the object is moving away from the starting point, and if the line is straight, it's moving at a constant speed).

### Question 3
# Brief Explanations:
In a speed - time graph ($y$ - axis: speed, $x$ - axis: time), the slope of the line is given by $m=\frac{\Delta y}{\Delta x}=\frac{\text{change in speed}}{\text{change in time}}$. A slope of zero means that $\frac{\text{change in speed}}{\text{change in time}} = 0$, which implies that the change in speed ($\Delta y$) is zero for any change in time ($\Delta x$). So the speed of the object remains constant over time. In other words, the object is moving at a constant speed (or if the speed is zero, it's at rest, but since the slope is zero, if the initial speed is non - zero, it stays non - zero and constant; if initial speed is zero, it stays zero).
# Answer:
A line with a slope of zero in a speed - time graph represents that the speed of the object is constant over time (the object is moving at a constant speed or is at rest if the speed value is zero).

### Question 4
# Brief Explanations:
Let's analyze the speed - time graph. At the start (time $t = 0$), the speed is $0$ (starts at the origin). Then the speed increases (the line goes up), which could represent the object accelerating, for example, a car starting from rest and pressing the gas pedal. Then the speed becomes constant (the horizontal line), which means the object is moving at a constant speed, like a car cruising on a highway at a steady speed. After that, the speed decreases (the line goes down), maybe the car is approaching a traffic light and slowing down. Finally, the speed becomes constant again (the last horizontal line), perhaps the car has reached a lower, constant speed, like moving in a traffic jam at a slow, steady pace.
Now, let's write a short story:
David got into his car at his house. At first, he was stopped (speed = 0). Then he started to accelerate as he merged onto the highway, so his speed increased. Once he was on the highway, he drove at a constant speed for a while. Then he saw a red light ahead, so he started to decelerate (his speed decreased). After stopping at the light, he started moving again at a slower, constant speed in the city traffic.

# Answer:
David got into his car at his house. At first, he was stopped (speed = 0). Then he started to accelerate as he merged onto the highway, so his speed increased. Once he was on the highway, he drove at a constant speed for a while. Then he saw a red light ahead, so he started to decelerate (his speed decreased). After stopping at the light, he started moving again at a slower, constant speed in the city traffic.

### Question 5
# Brief Explanations:
The graph is a distance - from - home - time graph. At the start, the distance from home is constant (the first horizontal line), which could mean the object (person) is at rest at a location away from home, like waiting at a bus stop. Then the distance from home starts to decrease (the line goes down), which means the person is moving towards home, maybe the bus has come and the person is traveling towards home. Then there is a horizontal line, which means the person has stopped for a while, perhaps to pick up a friend on the way. Then the distance from home decreases again, meaning the person is moving towards home again, and finally, the distance from home becomes $0$, which means the person has reached home.
Now, let's write a short story:
Sarah was at a coffee shop, which was a certain distance from her home. She waited at the coffee shop for a while (distance from home remained constant). Then she started to walk towards her home (distance from home started to decrease). On the way, she stopped to chat with a neighbor (distance from home remained constant for a short time). After that, she continued walking towards home until she finally reached her front door (distance from home became 0).

# Answer:
Sarah was at a coffee shop, which was a certain distance from her home. She waited at the coffee shop for a while (distance from home remained constant). Then she started to walk towards her home (distance from home started to decrease). On the way, she stopped to chat with a neighbor (distance from home remained constant for a short time). After that, she continued walking towards home until she finally reached her front door (distance from home became 0).

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