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What does the area under a force-extension graph represent?
The area under a graph of force against distance (or extension, if it's a spring) represents the work done by that force. Since it sounds like you're talking about a spring, you should know that the area would represent the work done to stretch the spring that distance, and also represents the amount of elastic potential energy contained by the spring.
How do you graph y equals 5x-4?
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What does an exponential graph and logistic graph of growth look like?
Yuo cannot include a graphical illustration here. Take a look at the Wikipedia, under "exponential function" and "logistic function". Basically, the exponential function increases faster and faster over time. The logistics function initially increases similarly to an exponential function, but then eventually flattens out, tending toward a horizontal asymptote.
How do you find the discriminant on a graph?
The discriminant is the expression under the square root of the quadratic formula.For a quadratic equation: f(x) = ax2 + bx + c = 0, can be solved by the quadratic formula:x = (-b +- sqrt(b2 - 4ac)) / (2a).So if you graph y = f(x) = ax2 + bx + c, then the values of x that solve [ f(x)=0 ] will yield y = 0. The discriminant (b2 - 4ac) will tell you something about the graph.(b2 - 4ac) > 0 : The square root will be a real number and the root of the equation will be two distinct real numbers, so the graph will cross the x-axis at two different points.(b2 - 4ac) = 0 : The square root will be zero and the roots of the equation will be a real number double root, so the graph will touch the x-axis at only one points.(b2 - 4ac) < 0 : The square root will be imaginary, and the roots of the equation will be two complex numbers, so the graph will not touch the x-axis.So by looking at the graph, you can tell if the discriminant is positive, negative, or zero.
How do you find the area under a curved graph without using the limiting chord process?
The integral function of calculus is the method for determining the area under a curve. The limiting chord process is the "simple" math understanding required to learn the "complex" function of "integration". BTW: the derivative function is a "cousin" of the integral function which is used to determine the slope of curve at a given point.
What is the area of a position time graph?
The area under a position-time graph represents the displacement of an object. It is calculated by finding the area between the curve of the graph and the time axis. The units of the area will be in distance units (e.g., meters, kilometers).
What does the slope of the graph represent and how does it varies in relation to the load position?
The slope of the graph represents the shear force at a particular point on a beam. As the load position changes along the beam, the magnitude of the shear force and therefore the slope of the graph varies accordingly. The slope will be steeper where the shear force is greater, such as under concentrated loads or at support points.
How do you interpret motion graphs?
Motion graphs, such as position-time or velocity-time graphs, can provide information about an object's motion. A horizontal line on a position-time graph indicates constant velocity, while a steeper slope indicates higher velocity. On a velocity-time graph, the slope represents acceleration (positive for speeding up, negative for slowing down). The area under a velocity-time graph represents displacement.
The area under a velocity-time graph represents?
The distance travelled over the time period represented by the area under the v-t graph between the end points.
Velocity is the slope of the displacement vs time graph?
Velocity is NOT the slope of the acceleration vs. time graph. Velocity is the area under the acceleration vs. time graph. Velocity is the slope of a position vs. time graph, though. For you Calculus Junkies, v = the integral of acceleration with respect to time.
How to convert a velocity time graph into a position time graph?
The position at time t (and therefore the height of the p-t graph) will be the area under the v-t curve between time 0 and t.
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 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.
Is displacement the slope of the velocity vs time graph?
No, displacement is the area under the velocity vs. time graph. The slope of a velocity vs. time graph represents acceleration.
Find position given velocity vs time graph?
To find the position from a velocity-vs-time graph, you need to calculate the area under the velocity curve. If the velocity is constant, the position can be found by multiplying the velocity by the time. If the velocity is changing, you need to calculate the area under the curve using calculus to determine the position.
What does the area under the force-distance graph represent?
The area under a force-distance graph represents the work done. It is equal to the force applied multiplied by the distance moved in the same direction as the force.
Explain x-t v-t graphs?
An x-t (position-time) graph shows how an object's position changes over time, while a v-t (velocity-time) graph shows how an object's velocity changes over time. In an x-t graph, the slope represents the object's velocity at that point, while in a v-t graph, the area under the curve represents the object's displacement.
