Because any translational motion problem can be separated into one or more 1-dimensional problems.

Problems are often analyzed this way - a complex problem can often be reduced to a set of simpler problems.

Scalars and vectors

A scalar is something that has only a magnitude while a vector has both a magnitude and a direction. In 1-dimension it's hard to tell them apart!

• Always draw a diagram of what you're trying to analyze.
  
  
• Choose an appropriate coordinate system. Define an origin (a reference point) and choose positive and negative directions.
  
  
• To fully describe motion you need to account for four things:
  time (scalar)
  position (vector)
  velocity (vector)
  acceleration (vector)

Displacement is a vector representing the distance traveled and specifying the direction.

If you start at position x_o and move to position x, your displacement Dx is defined as:

Example

If you move 5 meters north, Dx = 5 m north.

Now go the other direction, with a displacement of 3 m south.

The total distance traveled is 8 m. What is your net displacement?

Dx₁ = +5 m north
Dx₂ = +3 m south = - 3 m north

Net displacement: Dx = Dx₁ + Dx₂ = +5 -3 = +2 m north

• Velocity is a vector representing how fast, and in what direction, something is traveling.
• Speed is a scalar. It is the magnitude of the velocity.
• Speed just represents how fast something is going.

Velocity is the rate of change of position

Average velocity:   vav

=

Dx Dt

=

xf - xi tf - ti

Instantaneous velocity: v

=

lim Dt ® 0

Dx Dt

The instantaneous velocity is the slope of the line on a position-versus-time graph.

If the velocity is constant the instantaneous velocity is equal to the average velocity.

• Acceleration is a vector representing how fast, and in what direction, something's velocity is changing.
• Acceleration is related to velocity the same way velocity is related to position.

Acceleration is the rate of change of velocity.

Average acceleration:   aav

=

Dv Dt

=

vf - vi tf - ti

Instantaneous acceleration: a

=

lim Dt ® 0

Dv Dt

The instantaneous acceleration is the slope of the line on a velocity-versus-time graph.

If the acceleration is constant the instantaneous acceleration is equal to the average acceleration.