Understanding how objects move can be easier with some simple equations. These equations help us figure out different parts of motion when things move at a steady rate of change. Here are the main equations to know:

1. Displacement equation:
   ( s = ut + \frac{1}{2}at^2 )

   • Here, ( s ) is how far something has moved.
   • ( u ) is the speed it started at.
   • ( a ) is the constant acceleration.
   • ( t ) is the time it has been moving.

2. Final velocity equation:
   ( v = u + at )

   • In this case, ( v ) is the final speed after some time.

3. Velocity-displacement equation:
   ( v^2 = u^2 + 2as )

   • This one helps connect speed and distance.

These equations make it quick to do calculations with just a few important numbers.

For example, let’s think about an object that starts from rest (so ( u = 0 )), and it speeds up at ( 2 , \text{m/s}^2 ) for ( 5 , \text{seconds} ). We can find:

• Displacement (how far it goes):
  ( s = 0 + \frac{1}{2} \cdot 2 \cdot (5^2) = 25 , \text{meters} ).

• Final velocity (how fast it is at the end):
  ( v = 0 + 2 \cdot 5 = 10 , \text{m/s} ).

In short, these equations help us predict how things move and make it easier to understand motion when the acceleration stays the same.