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Rate is considered distance because if your rate is 5mph, your going 5 miles in 1 hour.
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Is it true that a straight diagonal line on a distance versus time graph indicates a constant speed?
Yes. The slope, or rate, is constant. The rate being represented is speed. If the slope is a negative constant, the object is losing distance (going towards) from the orgin at at a constant speed.
How is a distance time graph be used?
To find the average speed or rate of something.(:
Does a straight diagonal line on a distance versus time graph indicate constant speed?
Yes. Speed is the rate at which distance changes over time. In calculus terms v = dx/dt, or the slope of the distance vs. time graph. If the slope of the distance vs. time graph is a straight line, the speed is constant.
What is a differential calculus?
To a great extent, differential calculus is concerned with the slopes of curves - or with things that can be graphically represented as slopes, such as speed (the speed graph is a curve in a distance vs. time graph).
Can a rate change and the slope of the line be different quantities?
The instantaneous rate change of the variable y with respect to x must be the slope of the line at the point represented by that instant. However, the rate of change of x, with respect to y will be different [it will be the x/y slope, not the y/x slope]. It will be the reciprocal of the slope of the line. Also, if you have a time-distance graph the slope is the rate of chage of distance, ie speed. But, there is also the rate of change of speed - the acceleration - which is not DIRECTLY related to the slope. It is the rate at which the slope changes! So the answer, in normal circumstances, is no: they are the same. But you can define situations where they can be different.
Is it true that a straight diagonal line on a distance versus time graph indicates a constant speed?
Yes. The slope, or rate, is constant. The rate being represented is speed. If the slope is a negative constant, the object is losing distance (going towards) from the orgin at at a constant speed.
How can you get speed and distance covered by a body from distance time graph?
To get speed from a distance-time graph, you would calculate the slope of the graph at a given point, as the gradient represents speed. To calculate total distance covered, you would find the total area under the graph, as this represents the total distance traveled over time.
Does the slope of a speed-versus-time graph represents acceleration?
No, the slope of a speed-versus-time graph represents the rate of change of speed, not acceleration. Acceleration is represented by the slope of a velocity-versus-time graph.
How is a distance time graph be used?
To find the average speed or rate of something.(:
What is Speed that doesn't Change over time?
Speed that doesn't change over time is known as constant speed. This means an object is moving at a consistent rate without accelerating or decelerating. It can be represented by a straight horizontal line on a distance-time graph.
Does a straight diagonal line on a distance versus time graph indicate constant speed?
Yes. Speed is the rate at which distance changes over time. In calculus terms v = dx/dt, or the slope of the distance vs. time graph. If the slope of the distance vs. time graph is a straight line, the speed is constant.
What is a differential calculus?
To a great extent, differential calculus is concerned with the slopes of curves - or with things that can be graphically represented as slopes, such as speed (the speed graph is a curve in a distance vs. time graph).
What is a time distance graph?
A distance vs time squared graph shows shows the relationship between distance and time during an acceleration. An example of an acceleration value would be 3.4 m/s^2. The time is always squared in acceleration therefore the graph can show the rate of which an object is moving
What is unchanging speed?
Unchanging speed, also known as constant speed, refers to an object moving at a consistent rate without speeding up or slowing down. This means the object covers the same amount of distance in the same amount of time over the course of its motion. Mathematically, constant speed can be represented by a straight horizontal line on a distance-time graph.
What is non uniform speed?
One that changes. For example: you driving a car in a city.
What is the formula for instantaneous speed?
Instantaneous speed is calculated as the rate of change of distance with respect to time at a specific moment, and is represented by the formula: Instantaneous speed = ds/dt, where ds is the change in distance and dt is the change in time.
Can a rate change and the slope of the line be different quantities?
The instantaneous rate change of the variable y with respect to x must be the slope of the line at the point represented by that instant. However, the rate of change of x, with respect to y will be different [it will be the x/y slope, not the y/x slope]. It will be the reciprocal of the slope of the line. Also, if you have a time-distance graph the slope is the rate of chage of distance, ie speed. But, there is also the rate of change of speed - the acceleration - which is not DIRECTLY related to the slope. It is the rate at which the slope changes! So the answer, in normal circumstances, is no: they are the same. But you can define situations where they can be different.
