EQUATIONS OF MOTION
EQUATIONS OF MOTION
The three equations of motion are: v = u + at, s = ut + (1/2)at², and v² = u² + 2as. These equations relate an object's initial velocity (u), final velocity (v), acceleration (a), time (t), and displacement (s) in situations with constant acceleration.
Understanding the Equations
v = u + at:
This equation relates final velocity (v) to initial velocity (u), acceleration (a), and time (t). It signifies that the final velocity is equal to the initial velocity plus the product of acceleration and time.
s = ut + (1/2)at²:
This equation relates displacement (s) to initial velocity (u), acceleration (a), and time (t). It states that displacement is the sum of the initial velocity times time and half the product of acceleration and the square of time.
v² = u² + 2as:
This equation relates final velocity (v) to initial velocity (u), acceleration (a), and displacement (s). It states that the square of the final velocity is equal to the sum of the square of the initial velocity and twice the product of acceleration and displacement.
Worked examples
Example 1: Finding Final Velocity
Solution :
A car starts from rest (initial velocity, u = 0 m/s) and accelerates at a constant rate of 2 m/s² for 5 seconds. What is its final velocity (v)?
Given: u = 0 m/s, a = 2 m/s², t = 5 s
Equation: v = u + at
Solution: v = 0 + (2 * 5) = 10 m/s. The car's final velocity is 10 m/s.
Example 2: Finding Displacement
A train is traveling at 20 m/s and accelerates at a constant rate of 1 m/s² for 10 seconds. How far does it travel during this time?
Solution :
Given: u = 20 m/s, a = 1 m/s², t = 10 s
Equation: s = ut + (1/2)at²
Solution: s = (20 * 10) + (0.5 * 1 * 10²) = 200 + 50 = 250 m. The train travels 250 meters.
Example 3:
A car accelerates from 10 m/s to a certain final velocity. During this acceleration, it travels 50 meters and has an acceleration of 2 m/s². What is the final velocity?
Solution :
Given: u = 10 m/s, s = 50 m, a = 2 m/s²
Equation: v² = u² + 2as
Solution: v² = 10² + (2 * 2 * 50) = 100 + 200 = 300. Therefore, v = √300 ≈ 17.32 m/s.
NOTE:
These equations are fundamental in kinematics, the study of motion. They apply to situations with constant acceleration.
Careful identification of given variables and proper equation selection are crucial for accurate calculations.