QUESTION IMAGE
Question
graphs to speed/time graphs
name ______
date ______
period ______
sketch an example of each of the labeled graphs below. write a sentence that explains the
difference between the distance vs. time graph and the speed vs. time graph.
| distance vs. time | objects type of motion | speed vs. time |
|---|---|---|
| (distance axis, time axis) | object accelerating (positive acceleration) | (speed axis, time axis) |
| (distance axis, time axis) | object slowing down (negative acceleration) | (speed axis, time axis) |
Response
1. Object moving at a constant speed
Distance vs. Time Graph:
- Explanation: When speed is constant, distance increases linearly with time (since \( \text{Distance} = \text{Speed} \times \text{Time} \), and speed is constant). So the graph is a straight line with a positive slope.
- Sketch: Draw a straight line starting from the origin (or a non - origin point if initial distance is non - zero) with a constant slope.
Speed vs. Time Graph:
- Explanation: If speed is constant, it does not change with time. So the graph is a horizontal (flat) line parallel to the time axis.
- Sketch: Draw a horizontal line at a constant speed value (e.g., if speed is 5 m/s, draw a line at \( y = 5 \) where \( y \) - axis is speed and \( x \) - axis is time).
2. Object accelerating (positive acceleration)
Distance vs. Time Graph:
- Explanation: For an accelerating object, the speed is increasing (\( \text{Speed}=\text{Initial Speed}+ \text{Acceleration}\times\text{Time} \)). Using the distance formula \( \text{Distance}=\text{Initial Speed}\times\text{Time}+\frac{1}{2}\text{Acceleration}\times\text{Time}^2 \), the distance - time graph is a parabola opening upwards (since the coefficient of \( \text{Time}^2 \) is positive). The slope of the distance - time graph (which represents speed) increases with time.
- Sketch: Draw a curve that starts with a gentle slope and becomes steeper as time increases (a parabola - like curve).
Speed vs. Time Graph:
- Explanation: Positive acceleration means speed increases with time. So the graph is a straight line with a positive slope (since \( \text{Speed}=\text{Initial Speed}+\text{Acceleration}\times\text{Time} \), and acceleration is constant for simple cases).
- Sketch: Draw a straight line starting from the initial speed value on the speed axis and increasing with time (positive slope).
3. Object slowing down (negative acceleration)
Distance vs. Time Graph:
- Explanation: When an object is slowing down (negative acceleration), the speed is decreasing (\( \text{Speed}=\text{Initial Speed}-\vert\text{Acceleration}\vert\times\text{Time} \)). The distance formula is \( \text{Distance}=\text{Initial Speed}\times\text{Time}-\frac{1}{2}\vert\text{Acceleration}\vert\times\text{Time}^2 \). The distance - time graph is a parabola opening downwards (the coefficient of \( \text{Time}^2 \) is negative), and the slope (speed) decreases with time.
- Sketch: Draw a curve that starts with a steep slope and becomes less steep as time increases (a downward - opening parabola - like curve, approaching a maximum distance if the object comes to rest).
Speed vs. Time Graph:
- Explanation: Negative acceleration means speed decreases with time. So the graph is a straight line with a negative slope (since \( \text{Speed}=\text{Initial Speed}-\vert\text{Acceleration}\vert\times\text{Time} \), for constant deceleration).
- Sketch: Draw a straight line starting from the initial speed value on the speed axis and decreasing with time (negative slope), possibly reaching zero speed if the object comes to rest.
Difference between Distance vs. Time and Speed vs. Time Graphs
- A distance - time graph shows how the position (distance) of an object changes over time. The slope of a distance - time graph represents the speed of the object.
- A speed - time graph shows how the speed of an object changes over time. The slope of a speed - time graph represents the acceleration of the object, and the area under a speed - time graph represents the distance traveled.
For example, in…
Snap & solve any problem in the app
Get step-by-step solutions on Sovi AI
Photo-based solutions with guided steps
Explore more problems and detailed explanations
1. Object moving at a constant speed
Distance vs. Time Graph:
- Explanation: When speed is constant, distance increases linearly with time (since \( \text{Distance} = \text{Speed} \times \text{Time} \), and speed is constant). So the graph is a straight line with a positive slope.
- Sketch: Draw a straight line starting from the origin (or a non - origin point if initial distance is non - zero) with a constant slope.
Speed vs. Time Graph:
- Explanation: If speed is constant, it does not change with time. So the graph is a horizontal (flat) line parallel to the time axis.
- Sketch: Draw a horizontal line at a constant speed value (e.g., if speed is 5 m/s, draw a line at \( y = 5 \) where \( y \) - axis is speed and \( x \) - axis is time).
2. Object accelerating (positive acceleration)
Distance vs. Time Graph:
- Explanation: For an accelerating object, the speed is increasing (\( \text{Speed}=\text{Initial Speed}+ \text{Acceleration}\times\text{Time} \)). Using the distance formula \( \text{Distance}=\text{Initial Speed}\times\text{Time}+\frac{1}{2}\text{Acceleration}\times\text{Time}^2 \), the distance - time graph is a parabola opening upwards (since the coefficient of \( \text{Time}^2 \) is positive). The slope of the distance - time graph (which represents speed) increases with time.
- Sketch: Draw a curve that starts with a gentle slope and becomes steeper as time increases (a parabola - like curve).
Speed vs. Time Graph:
- Explanation: Positive acceleration means speed increases with time. So the graph is a straight line with a positive slope (since \( \text{Speed}=\text{Initial Speed}+\text{Acceleration}\times\text{Time} \), and acceleration is constant for simple cases).
- Sketch: Draw a straight line starting from the initial speed value on the speed axis and increasing with time (positive slope).
3. Object slowing down (negative acceleration)
Distance vs. Time Graph:
- Explanation: When an object is slowing down (negative acceleration), the speed is decreasing (\( \text{Speed}=\text{Initial Speed}-\vert\text{Acceleration}\vert\times\text{Time} \)). The distance formula is \( \text{Distance}=\text{Initial Speed}\times\text{Time}-\frac{1}{2}\vert\text{Acceleration}\vert\times\text{Time}^2 \). The distance - time graph is a parabola opening downwards (the coefficient of \( \text{Time}^2 \) is negative), and the slope (speed) decreases with time.
- Sketch: Draw a curve that starts with a steep slope and becomes less steep as time increases (a downward - opening parabola - like curve, approaching a maximum distance if the object comes to rest).
Speed vs. Time Graph:
- Explanation: Negative acceleration means speed decreases with time. So the graph is a straight line with a negative slope (since \( \text{Speed}=\text{Initial Speed}-\vert\text{Acceleration}\vert\times\text{Time} \), for constant deceleration).
- Sketch: Draw a straight line starting from the initial speed value on the speed axis and decreasing with time (negative slope), possibly reaching zero speed if the object comes to rest.
Difference between Distance vs. Time and Speed vs. Time Graphs
- A distance - time graph shows how the position (distance) of an object changes over time. The slope of a distance - time graph represents the speed of the object.
- A speed - time graph shows how the speed of an object changes over time. The slope of a speed - time graph represents the acceleration of the object, and the area under a speed - time graph represents the distance traveled.
For example, in a distance - time graph, a straight line means constant speed, while in a speed - time graph, a straight line means constant acceleration (positive, negative, or zero).