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.
Start Here
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