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Q: Short-lived velocity defined as the slope of the tangent line at a given point on a curve?
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What t-word is defined in geometry as a straight line that touches a curve?

tangent


What t-word is defined in geometry as a strait line that touches a curve?

tangent


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

No, it is instantaneous acceleration.


What T-word is defined in geometry as a straight line that touches a curve but continue on with crossing?

Tangent


What is initial tangent?

The tangent (of a curve) is a vector that is tangent (perpendicular to the normal), i.e. the instantaneous velocity of the curve at a specific point. As such, the initial tangent is the initial velocity of the curve at the point where t=0. Stated in other terms, the tangent is the slope of the line at a point. This is expressed (in two dimensions, but applicable to higher dimensions), as the line that has x and y coordinates equal to the point of tangency, and slope equal to the limit of delta y over delta x as delta x (and delta y) approaches zero.


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

it measures the magnitude of acceleration, but it can't tell you the direction of the acceleration.


What T-word is defined in geometry as a straight line that that touches a curve but continues on without crossing?

It is a tangent line


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

the slope of a tangent to the curve of a V vs T graph is acceleration at that point in time. the derivative of the function for the V vs T graph would be the function for acceleration at any given time


How do you find the slope of an Indifference curve?

You find the tangent to the curve at the point of interest and then find the slope of the tangent.


Find an equation of the line tangent to the curve defined by x^2+3xy+y^4=32 at the point (2,2)?

55


The slope of a line drawn tangent to a point on the curve of a position vs time graph describes what concept?

It is the instantaneous velocity, if it were a graph with velocity over time, then it would be acceloration