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The area between the graph and the x-axis is the distance moved. If the velocity is constant the v vs t graph is a straight horizontal line. The shape of the area under the graph is a rectangle.
For constant velocity, distance = V * time. Time is the x-axis and velocity is the y-axis.
If the object is accelerating, the velocity is increasing at a constant rate. The graph is a line whose slope equals the acceleration. The shape of the graph is a triangle. The area under the graph is ½ * base * height. The base is time, and the height is the velocity.
If the initial velocity is 0, the average velocity is final velocity ÷ 2.
Distance = average velocity * time.
Distance = (final velocity ÷ 2) * time, time is on the x-axis, and velocity is on the y-axis.
(final velocity ÷ 2) * time = ½ time * final velocity
...½ base * height = ½ time * final velocity
Area under graph = distance moved
Most velocity graphs are horizontal lines or sloping lines.
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RafaTo calculate distance from a velocity-time graph, you would find the area under the curve, as this represents the displacement or distance traveled. If the graph is above the time axis, calculate the area above the time axis, and if it dips below, calculate the area below the time axis. Summing these two areas will give you the total distance traveled.
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When do two different distance-time graphs have matching velocity-time graphs?
Two different distance-time graphs have matching velocity-time graphs when the slope of the distance-time graph represents the velocity in the velocity-time graph, as velocity is the derivative of distance with respect to time. This means that the steeper the distance-time graph, the greater the velocity on the velocity-time graph at that point.
How is the velocity-time graph related to the distance traveled?
The distance traveled can be calculated by finding the area under the velocity-time graph. The slope of the graph at any point represents the acceleration of the object. The steeper the slope, the greater the acceleration.
How do you go from a position graph to a velocity graph?
To go from a position graph to a velocity graph, you can calculate the slope of the position graph at each point. The slope at any given point on a position vs. time graph represents the velocity at that specific time. Therefore, the velocity graph would be a plot of the slopes at each point on the position graph.
Can a position time graph be created from a velocity time graph?
Yes, a position-time graph can be created from a velocity-time graph by integrating the velocity values over time. By finding the area under the velocity-time curve, you can determine how the position of an object changes over time.
How do you figure out the starting point of a distance vs time graph when given the velocity vs time graph and a function?
To find the starting point of a distance vs time graph from a velocity vs time graph and a function, you would integrate the velocity function to find the displacement function. The starting point of the distance vs time graph corresponds to the initial displacement obtained from the displaced function.
