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VELOCITY

VELOCITY. Distance. Acceleration. AP 2003 FRQ#4 ( Form B). Q: A particle moves along the x-axis with velocity at time t ≥ 0 given by v(t)= -1+e 1-t. Find the acceleration of the particle at time t=3. Is the speed of the particle increasing at time t=3? Give a reason for your answer.

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VELOCITY

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  1. VELOCITY Distance Acceleration AP 2003 FRQ#4 ( Form B)

  2. Q: A particle moves along the x-axis with velocity at time t≥0 given by v(t)= -1+e1-t • Find the acceleration of the particle at time t=3. • Is the speed of the particle increasing at time t=3? Give a reason for your answer. • Find all values of t at which the particle changes direction. Justify your answer. • Find the total distance traveled by the partcle over the time interval 0≤t≤3.

  3. Find the acceleration of the particle at time t=3. • a(t)=v'(t)<-- first derivative of the velocity • v(t)= -1+e1-t • a(t)=v'(t)= e1-t• -1= -e1-t • since t= 3 • a(3)= -e1-3= -e-2

  4. Is the speed of the particle increasing at time t=3? Give a reason for your answer. • speed is increasing when both velocity and acceleration have the SAME sign. • time = 3 • v(t)= -1+e1-t • v(3)= -1+e-2=-.865<-- Negative • a(t)=-e1-t • a(3)=-e-2= -.135<-- Negative • Both velocity and acceleration are negative therefore the speed is increasing.

  5. Find all values of t at which the particle changes direction. Justify your answer. • The particle changes direction when the velocity changes sign. • The velocity changes sign at t=1 ( from positive to negative) • Therefore the particle changes direction at time=1.

  6. Find the total distance traveled by the partcle over the time interval 0≤t≤3. • The total distance is the absoulte value of the anti-derivative of the velocity function. • total distance= ∫ I v(t) I dt • the time interval is from 0 to 3 • a=0, b=3 • DISTANCE=

  7. Work Cited • AP Calculus AB 2003 Free Response Questions Form B • http://apcentral.collegeboard.com/apc/public/repository/ap03_frq_calculus_ab__23063.pdf • Samply Responses for Q4 • http://apcentral.collegeboard.com/apc/public/repository/ap03_calculusab_formb_27988.pdf • AP CAP Calculus AB 2003 Form B scoring guidelines • http://apcentral.collegeboard.com/apc/members/repository/ap03_sg_calculus_ab_b_26473.pdf • Online graphing calculator • http://www.coolmath.com/graphit/ • http://www.mathworksheetsgo.com/tools/free-online-graphing-calculator.php

  8. ANY QUESTIONS?

  9. THE END!

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