Motion in One Dimension

1
Motion in One Dimension

• Kinematics
• (continued)

2
Describing Motion in 1-D

• Consider uniform acceleration (a constant)
• Goal is finding equations for
• Velocity as a function of time
• Displacement as a function of time
• Velocity as a function of displacement
• Use definitions for average acceleration and
  average velocity

3
Motion in 1-D with Uniform a

• Procedure
• Algebraically manipulate equations
• Remove all f subscripts
• Change all i subscripts to 0
• Let t0 0
• First derive expression v as function of t

4
Evaluate Velocity for Uniform a

• Velocity is linear function of time (v v0 at)
• Average velocity is midway between v and v0

5
Summary ofMotion in 1-D with Constant a
When a 0 these equations correspond to uniform
motion (v constant)
6
Freely Falling Objects

• The only acceleration is due to gravity
• There is no air resistance to impede the motion
• Gravity provides a constant (uniform)
  acceleration near the surface of the earth
• Replace x with y to indicate vertical position in
  equations of motion

7
Summary of Free Fall Equations
Up is the positive y direction.
8
Typical Vertical 1-D Problems

• Dropping objects
• Propelling objects straight up
• What you might be asked
• Find velocity at certain times or displacements
• Find time for a certain displacement or velocity
• Find height at a certain time or velocity
• Find the maximum height