# Speed vs. Velocity

## Key Formulas

 v velocity m/s Δx displacement m Δt elapsed time s
 s speed m/s d distance m Δt elapsed time s

## Tips to Remember

• Velocity is a vector quantity. That means it has both magnitude (how fast) and direction. Sometimes the direction isn’t obviously given, but it’s buried in the sign of the velocity. For example, a velocity of 6 m/s doesn't have an obvious direction like up or east, but it is in the positive direction, as opposed to -6 m/s, which would be in the opposite direction.
• Speed is a scalar quantity. That means that it has only magnitude; the direction is not included. Speed will always be positive, since a negative speed would imply a direction.
• Since velocity is a vector, it depends on displacement, which is also a vector. Similarly, speed depends on distance, which is a scalar like itself. Displacement takes direction into account, but distance does not. That means that if someone walks 7 m east, then 4 m west, her displacement is 7 + (-4), or 3 m. The distance she covers is 7 + 3, or 10 m. The direction change in the 4 m leg caused a negative displacement, but not a negative distance, since distance is always positive.
• The displacement is the difference between the object’s starting and ending positions. That means that if someone walks around a track and returns to her starting point, her displacement is zero.