marin mersenne 1588 1648 marin mersenne 1588 1648 marin mersenne was a french monk who is best...

Marin Mersenne1588 – 1648

Marin Mersenne was a French monk who is best known for his role as a clearing house for correspondence between eminent philosophers and scientists and for his work in number theory.

Velocity is the first derivative of position.

Example 1: Free Fall Equation

21 2

s g t

GravitationalConstants:

2

ft32 sec

g

2

m9.8 sec

g

2

cm980 sec

g

21 32 2

s t

216 s t

32 dsV tdt

Speed is the absolute value of velocity.

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Acceleration is the derivative of velocity.

dvadt

2

2

d sdt

Example: 32v t32a

If distance is in: feet or meters

Velocity would be in:feet meters or sec sec

Acceleration would be in:ft

sec sec

2

ftsec

msecor sec

2

msec

It is important to understand the relationship between velocity, acceleration and the behavior of the particle.

Velocity Acceleration Behavior of Particle

Positive Positive Speeding Up

Positive Negative Slowing Down

Negative Positive Slowing Down

Negative Negative Speeding Up

Zero Positive or Negative Stopped

Positive or Negative Zero Constant Speed

Example 1:3 2Consider the position function ( ) 6.4 9.1 moving

horizontally. Time is measured in seconds ( 0) and position in feet.a) Find the velocity and acceleration functions.b) What is the velocity

s t t t tt

and direction after 2.351 seconds and 4.957 seconds?c) When is the particle stopped?d) When is the particle moving left/right?e) When is the particle speeding up/slowing down?f) How far did the particle travel from start to 4 seconds?

p