Question

Derive the 3 equation of motion

Answer 1

The three equations of motion can be derived by considering the relationships between displacement (s), velocity (v), acceleration (a), and time (t).

1. v = u + at
This equation represents the relationship between initial velocity (u), acceleration (a), time (t), and final velocity (v). It can be derived by rearranging the equation of motion:
v = u + at

2. s = ut + (1/2)at^2
This equation represents the relationship between initial velocity (u), displacement (s), acceleration (a), and time (t). It can be derived using the formula for average velocity:
s = (u + v)/2 * t
Substitute v = u + at:
s = ((u + u + at)/2)*t
s = (2u + at)/2)*t
s = ut + (1/2)at^2

3. v^2 = u^2 + 2as
This equation represents the relationship between initial velocity (u), final velocity (v), acceleration (a), displacement (s). It can be derived from the equation of motion:
v = u + at
Squaring both sides:
v^2 = (u + at)^2
Expand the right side:
v^2 = u^2 + 2uat + a^2t^2
Since a^2t^2 is negligible in comparison with other terms, the equation simplifies to:
v^2 = u^2 + 2as

These three equations are fundamental in classical mechanics and describe the motion of objects under constant acceleration.