Derivation of Second Equation of Motion
The second equation of motion is given as:
v = u + at
Step 1: Define Variables
We define the following variables:
- u: Initial velocity of the object
- v: Final velocity of the object
- a: Acceleration of the object
- t: Time taken for the object to travel from initial velocity to final velocity
Step 2: Derive Average Velocity
The average velocity of the object is given by:
avg. velocity = (u+v)/2
Step 3: Derive Displacement
The displacement of the object is given by:
displacement = avg. velocity * t
displacement = (u+v)/2 * t
Step 4: Derive Second Equation of Motion
The second equation of motion is derived by using the following equation:
v^2 = u^2 + 2ad
where, d is the displacement of the object.
Substituting the value of displacement from step 3, we get:
v^2 = u^2 + 2a(u+v)/2 * t
v^2 = u^2 + at(u+v)
Dividing both sides by v-u, we get:
v+u = at
or, v = u + at
Step 5: Conclusion
Thus, the second equation of motion is derived using the calculus method.