Phyics C (Kinematics)

Velocity is the _____ at which _____ changes.

rate; position

Write a formula used to find slope between two points.

(y2 - y1)/(x2 - x1)

A formula like slope-intercept form is used to find _____ velocity rather than instantaneous velocity.

average

When writing any figure, you should always include ____, and most of the time, round to ____ decimal places, even if the last decimal place is ____.

units; three; zero

A derivative is an instantaneous _______.

rate of change

A ____ line is a straight line which matches the slope of a curve at one point.

tangent

A derivative provides the ____ of a tangent line.

slope

When using the Power Rule to find a derivative, the exponent _____ by 1 and the ______ gets multiplied by the old exponent.

decreases; coefficient

Velocity is the first derivative of _____.

position

______ is the first derivative of velocity an the _____ derivative of _____.

acceleration; second; position

5th

The maximum value of a function will usually occur when its ______ is equal to _____.

derivative; zero

Later, the students analyze their data and determine that v₀ = 4.1 m/s. Using the same launcher as in part (a) the students set up the experiment shown in Figure 3. They disagree on the formula relating the horizontal distance D that the sphere travels to the angle θ_L above the horizontal it is launched from. Students 1 and 2 make the following claims.

Student 1: “I found this formula for D on the Internet: D = v02gsin(2θ_L).”

Student 2: “I think there is an error in that formula. I would expect D to be proportional to sin(θ_L), not sin(2θ_L).”

To determine who is correct, they write the following mathematical model: D = v02gsin(nθ_L), where n is a positive constant and may or may not be an integer. The students wish to determine n experimentally.

(c) iii. Draw a straight line that best represents the data.