Free fall and projectile motion are two kinds of movement that show us how things move in a straight line.

Free Fall:

• When an object is in free fall, it speeds up constantly because of gravity. This acceleration is about 9.81 meters per second squared, going downward.
• We can use these simple equations to understand its motion:
  • Velocity (how fast it's going): ( v = gt )
  • Displacement (where it ends up): ( s = \frac{1}{2}gt^2 )

Projectile Motion:

• A projectile is anything thrown or launched into the air. It moves in a curved path because of gravity and its starting sideways speed.
• The up-and-down movement is like free fall, using the same gravity of 9.81 meters per second squared.
• The sideways movement is steady, moving at a constant speed because nothing is pushing it to speed up or slow down.
• Here are some key equations for projectile motion:
  • Vertical displacement (how far it goes up or down): ( y = v_{0y}t - \frac{1}{2}gt^2 )
  • Horizontal displacement (how far it goes sideways): ( x = v_{0x}t )

Both free fall and projectile motion help us understand how objects move in a straight line. They show clear relationships between where something is (displacement), how fast it's going (velocity), and how it speeds up or slows down (acceleration).