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The rate of Change in acceleration.

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Ophelia West

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What physical property does the slope of a velocity time graph represent?

velocity.


What is the relationship between slope of a tangent line and velocity?

The slope of any line is rise/run, or change in y divided by change in x. On a distance-time curve, time is the variable on the x axis, and distance is the variable on the y axis. This means that when a tangent is drawn at any point on the curve, its slope becomes change in distance divided by change in time, for example, m/s, km/h, etc. These units align with the units for velocity, and therefore the slope of the tangent line on a distance-time curve is the velocity.


What is instantaneous slope?

The instantaneous slope of a curve is the slope of that curve at a single point. In calculus, this is called the derivative. It also might be called the line tangent to the curve at a point. If you imagine an arbitrary curve (just any curve) with two points on it (point P and point Q), the slope between P and Q is the slope of the line connecting those two points. This is called a secant line. If you keep P where it is and slide Q closer and closer to P along the curve, the secant line will change slope as it gets smaller and smaller. When Q gets extremely close to P (so that there is an infinitesimal space between P and Q), then the slope of the secant line approximates the slope at P. When we take the limit of that tiny distance as it approaches zero (meaning we make the space disappear) we get the slope of the curve at P. This is the instantaneous slope or the derivative of the curve at P. Mathematically, we say that the slope at P = limh→0 [f(x+h) - f(x)]÷h = df/dx, where h is the distance between P and Q, f(x) is the position of P, f(x+h) is the position of Q, and df/dx is the derivative of the curve with respect to x. The formula above is a specific case where the derivative is in terms of x and we're dealing with two dimensions. In physics, the instantaneous slope (derivative) of a position function is velocity, the derivative of velocity is acceleration, and the derivative of acceleration is jerk.


What is a derivative graph?

A derivative graph tracks the slope of a function.


What does the slope of the graph represent?

The slope of the graph represents distance over time. The distance is represented by "X," and the time is represented by "Y."

Related Questions

What does the slope of a curve represent on a velocity-versus-time graph represent?

The slope of the speed/time graph is the magnitude of acceleration. (It's very difficult to draw a graph of velocity, unless the direction is constant.)


What does the slope of they curve on a velocity-versus-time graph represent?

The rate of change in accelleration.


What does the slope of the curve on a distance v time graph represent?

The slope of the curve at each point on thegraph is the speed at that point in time. (Not velocity.)


What does a slope of a time graph represent?

The slope of a velocity-time graph represents acceleration.


What does slope of a speed time graph represent?

The slope of a velocity-time graph represents acceleration.


What physical property does the slope of a velocity time graph represent?

velocity.


If the velocity is constant describe the slope of the graph on a position vs. time graph.?

If velocity is constant, the slope of the graph on a position vs. time graph will be a straight line. The slope of this line will represent the constant velocity of the object.


Does the slope of a position time graph represent average velocity or rate of change of velocity?

The tangent at a point on the position-time graph represents the instantaneous velocity. 1. The tangent is the instantaneous slope. 2. Rather than "average" velocity, the slope gives you "instantaneous" velocity. The average of the instantaneous gives you average velocity.


In what kind of graph can you identify velocity?

Velocity can be identified in a position-time graph through the slope of the curve at any given point. The slope represents the velocity at that particular moment in time. A steeper slope indicates a higher velocity, while a shallow slope indicates a lower velocity.


What does the slope of the tangent to the curve on a velocity-time graph measure?

The slope of the tangent to the curve on a velocity-time graph represents the acceleration of an object. Positive slope indicates acceleration in the positive direction, negative slope indicates acceleration in the negative direction, and zero slope indicates constant velocity.


Is Average velocity the slope of the line tangent to the curve on a velocity time graph at a specific instant of time?

No, average velocity is the total displacement divided by the total time taken. The slope of the tangent to the curve on a velocity-time graph at a specific instant of time gives the instantaneous velocity at that moment, not the average velocity.


In position vs. time graph what variable does slope represent?

The slope of a line on a position vs. time graph would represent the a velocity of the object being described.