**Equations of Motion**

Equations of motion are mathematical formulas that describe the relationship between an object's position, velocity, and acceleration. These equations are derived from Newton's laws of motion and are essential tools for solving problems related to motion.

**The Three Equations of Motion**

There are three fundamental equations of motion, which are commonly used to solve problems in physics:

1. **First Equation of Motion (v = u + at):**
- This equation relates the final velocity (v) of an object to its initial velocity (u), acceleration (a), and time (t).
- It states that the final velocity of an object is equal to its initial velocity plus the product of acceleration and time.
- The equation assumes constant acceleration.

2. **Second Equation of Motion (s = ut + (1/2)at^2):**
- This equation relates the displacement (s) of an object to its initial velocity (u), time (t), and acceleration (a).
- It states that the displacement of an object is equal to its initial velocity multiplied by time, plus half the product of acceleration and the square of time.
- This equation is applicable when the acceleration is constant.

3. **Third Equation of Motion (v^2 = u^2 + 2as):**
- This equation relates the final velocity (v) of an object to its initial velocity (u), acceleration (a), and displacement (s).
- It states that the final velocity of an object squared is equal to its initial velocity squared plus twice the product of acceleration and displacement.
- This equation is derived by combining the first and second equations of motion.

**Solving Problems Using Equations of Motion**

To solve problems using equations of motion, follow these steps:

1. Identify the known quantities:
- Determine which variables are given in the problem statement.
- Typically, you will have values for initial velocity, acceleration, and time or displacement.

2. Determine the unknown quantity:
- Identify the variable that needs to be solved for (e.g., final velocity, displacement, or time).

3. Choose the appropriate equation:
- Based on the known quantities and the unknown quantity, select the equation that can be rearranged to solve for the desired variable.

4. Substitute the values:
- Plug in the known values into the chosen equation.

5. Solve for the unknown variable:
- Rearrange the equation algebraically to isolate the unknown variable.

6. Calculate the numerical value:
- Substitute the known values into the equation and perform the necessary calculations to find the numerical value of the unknown variable.

7. Check the units and significant figures:
- Ensure that the units of the final answer are consistent with the problem's requirements.
- Round the answer to the appropriate number of significant figures.

By following these steps and utilizing the equations of motion, you can successfully solve problems related to the motion of objects. Remember to pay attention to the given information and use the appropriate equation for the specific scenario.