Tangents, velocities and other rates of change

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In summary, a tangent is a line that touches a curve at only one point, without crossing over or intersecting the curve. It is different from a secant, which intersects the curve at two points. Velocity is a measure of the rate of change of an object's position over time, and it is a vector quantity. To calculate velocity, you can divide the change in position by the change in time, or use other mathematical formulas. A rate of change is a measure of how one quantity changes in relation to another quantity, and it can be expressed as a slope, derivative, or other mathematical formula.
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bobsmith76
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I really don't see how they went from step 1 to step 2 in this example. Any advice would help.

Screenshot2012-01-22at81825PM.png
 
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I understand this problem now.
 

FAQ: Tangents, velocities and other rates of change

1. What is a tangent?

A tangent is a line that touches a curve at only one point, without crossing over or intersecting the curve.

2. How is a tangent different from a secant?

A secant is a line that intersects a curve at two points, whereas a tangent only touches the curve at one point.

3. What is velocity?

Velocity is a measure of the rate of change of an object's position over time. It is a vector quantity, meaning it has both magnitude and direction.

4. How do you calculate velocity?

Velocity can be calculated by dividing the change in position by the change in time. This can be expressed as the slope of a line on a position-time graph, or as the derivative of the position function with respect to time.

5. What is a rate of change?

A rate of change is a measure of how one quantity changes in relation to another quantity. It can be expressed as a slope, derivative, or other mathematical formula.

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