2.1- The Tangent and Velocity Problems
Average velocity in meters
4.9(₁t)² - 4.9(₂t)² —————————- ₁t - ₂t
Tangent Line
A line in the plane of a circle that intersects the circle in exactly one point.
secant line
A line that intersects a circle in two points
average velocity
the rate of change of an object's position with respect to a frame of reference, and is a function of time
Limit
the slope of the tangent line is the ..... of the slopes of the secant line
instantaneous velocity
the velocity of an object at some instant or at a specific point in the object's path
tangent line
To find an instantaneous velocity, calculate the slope of the ....
Displacement/time
Average velocity formula
Once
By definition, a line tangent to a curve would "touch " the curve how many times?
discontinuity
If a is in the domain of the function, there shouldn't be any....
Step 1: Secant line PQ, where P is also the tangent line. Repeatedly select points Q closer and closer to P and calculate the slopes in a graph. Step 2: The number the slopes of the secant lines approach = slope of the tangent line. Step 3: Leave equation of the tangent line in point slope form.
Steps to finding the slope of a tangent line
Step 1: Secant line P and Q. Find the two closest points of PQ to the right and left of point P Step 2: Calculate slope by averaging the two slopes of the secant lines.
Steps to finding the slope of a tangent line (word problems)
Instantaneous velocity
The "limiting" value of the average velocities over shorter and shorter time periods
Average Velocity
The average slope between two points in time will give you the ...... between those two points in time
limit of the slopes of the secant lines
The slope of the tangent line is the..
slope
The steepness of a line on a graph
Slope
The tangent line is useful because it allows us to find the ...... of a curved function at a particular point on the curve
Secant line
To find an average velocity, calculate the slope of the ....
point slope form
What form is the equation of a tangent line written in?
Limit
as far as something can go
Galileo's law
s(t) = 4.9t²
The distance fallen after t seconds
s(t) in regards to Galileo's Law is read as...
Displacement
the change in position of an object