Question

derivation of the first equation of motion by calculus method​

Answer 1

Given:

The first equation of motion  

To find:

Derivation of the first equation of motion by calculus method​

Solution:

From given, we have to derive the first equation of motion by calculus method​

we know that the acceleration is the rate of change of velocity

so, we get,

a = dv/dt

⇒ dv = a dt

integrating on both the sides, we get,

∫ [u to v] dv = ∫ [0 to t] a dt

⇒ ∫ [u to v] dv = a × ∫ [0 to t] 1 dt

upon integration, we get,

v - u = at

v = u + at

Hence the required first equation of motion by calculus method​