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Lecture

# 5.4 Integration & Anti-derivatives Indefinite Integrals Question #4 (Medium)

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Department
Mathematics
Course
MAT136H1
Professor
All Professors
Semester
Winter

Description
5.4 Integration & Anti-derivatives Indefinite Integrals Question #4 (Medium): Working With Acceleration, Velocity, Displacement, and Distance Strategy Acceleration is the derivative of velocity. Velocity is the derivative of displacement. Thus, ( ) ( ) , and ( ) ( ) . ∫ ∫ Displacement is the net distance travelled, so ∫ ( ) . But Distance is the total distance travelled, so ∫ | ( )| . Sample Question The given acceleration (in ) and the initial velocity (in ) describe a particle moving along a line. ( ) , ( ) , 1) Find the velocity at time . 2) Find the total distance travelled during the given time interval. Solution 1) Velocity is the anti-derivative of acceleration: Thus, ( ) ∫ ( ) ∫ ( ) a. Since ( ) , then ( ) ( ) . So the constant factor . So the velocity function at
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