Question

Derive equations of motion by using integration method?​

Answer 1

Answer:

First, consider a body moving in a straight line with uniform acceleration. Then, let the initial velocity be u, acceleration be a, time period be t, velocity be v, and the distance travelled be S. The equation of motions derivation can be done in three ways which are: ... Derivation of Motion by Calculus Method.

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Answer 2

Derive equations of motion by using integration method.

• a constant function of the coordinates along a phase-space trajectory. If an integral of motion can be found, the number of degrees of freedom of a dynamical system, such as the Duffing differential equation, can be reduced by one.
• which equations you wish to derive will depend. As an illustration, try this:
• Starting with speed(v) = starting speed(u) + acceleration/time, you can determine the total distance travelled (let's say D) by integrating over t using v.dt = u.dt + a.t.dt.
• D=u.t + (at^2)/2

distance traveled = average velocity * time taken

distance traveled = ( ( initial velocity + final velocity ) / 2 ) * time taken

S = ( ( u + v ) / 2 ) * t

From 1. v = u + a t

S = ( ( u + ( u + a t ) ) / 2 ) *t

S = ( ( 2 u + a t ) / 2 ) * t

S = ( ( 2 u / 2 ) + ( a t / 2 ) ) * t

S = ( u + a t / 2 ) * t

S = u t + ( a t^2 ) / 2

S = u t + ( a t^2 ) / 2

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