calc alternative assessmentc

7/27/2019 Calc Alternative Assessmentc

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CALCULUS ALTERNATIVE

ASSESMENTBy: Stephen Macaspac


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Distance Versus Displacement

Question:The man sitting in his lawnchair decided that he would walk over to pickthe flower. He walked at a velocity of v(t)=sin(t)miles per hour to get the

flower and return to his chair which took him a total of 6.28 hours. Whatis the man's displacement from t=0 to t=6.28? Using this Formula, whatis his total distance traveled?


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Distance Vs. Displacement

Displacement

How far something is from

the start after it has traveled

Distance

Length. A measurement of

how far through space.


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Distance Vs. Displacement

Finding Displacement1. Identify what is given

1. Velocity Equation: v(t)=sin(t)

2. Upper Bound: 6.28 hours

3. Lower Bound 0 hours

2. With Ti inspire Calculator:

1. Find definite integral template

2. Plug in Upper/Lower Bound and Equation

3. Answer is the displacement

3. Without Calculator

1. Anti Derive Equation

1. -cos(x)

2. Plug in Upper and Lower bounds

3. Solve For the Displacement

4. Answer: 0 m

Finding Distance1. Identify what is given

1. Velocity Equation: v(t)=sin(t)

2. Upper Bound: 6.28 hours

3. Lower Bound 0 hours

2. With Ti inspire Calculator:


2. Plug in Upper/Lower Bound and Equation

1. Find absolute value template and place equation inside

3. Answer is the displacement


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Average Velocity

Question: A ball is thrown into the air at a velocity of 49

ft/s. Its height in feet after t seconds is given by y=49t-

10t2


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Average Velocity

Definition: averagevelocityis just net distance

traveled divided by time


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Average Velocity

With Ti Inspire

1. Definite integral of velocity equation

1. Choose two different points as upper and lowerbound

1. 0.01 seconds

2. 0.005 seconds


1. Plug in upper and lower bound

2. Plug in equation

3. Answer = 0.00183

3. Take the answer and divide by thedifference of the time periods

1. 0.00183/0.01-0.005

2. Average Velocity=0.36 ft/s

Without Calculator

1. Definite integral of velocity equation

1. Choose two different points as upper and lowerbound

1. 0.01 seconds

2. 0.005 seconds

2. Integrate

1. Anti derive equation

1. (49x2/2)-(10x3/3)

2. Plug in upper and lower bound

1. (49(0.01)2/2)-(10(0.01)3/3)-(490(0.005)2/2)-

(10(0.005)3

/3)

3. Solve

1. 0.00183

3. Take the answer and divide by the difference ofthe time periods

1. 0.00183/0.01-0.005

2. Average Velocity=0.36 ft/s


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Related Rates

Question: A car is traveling north toward an intersection at a rate of 60 mph

while a truck is traveling east away from the intersection at a rate of 50 mph.

Find the rate of change of the distance between the car and truck when the

car is 3 miles south of the intersection and the truck is 4 miles east of the

intersection.

Letx= distance traveled by the truck

y= distance traveled by the car

z = distance between the car and truck


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Related Rates

Definition: related rates problems involve finding a

rate at which a quantity changes by relating that

quantity to other quantities whose rates of changeare known.


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Related Rates

Overview Process

1. Write the known rates as a derivative

1. rate of change of the truck is dx/dt= 50 mph

2. rate of change of the car is dy/dt= 60 mph

2. Write the unknown rate as a derivitive

1. Rate of change between the distance and the truck dz/dt=?

3. Write the equation that relates to both 1 and 2

1. x2 + y2 = z2

4. Implicitly derive the equation with respect to t

1. substitute all know distance and rates and solve for 2

5. Interpret the question asked

calc alternative assessmentc

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