Question

S=ut+1/2at^2 derive by integration method

Answer 1

Answer:

hence proved

Explanation:

hope u will get the answer...........

Answer 2

Answer:

The final equation is:

S = ut + (1/2)at^2, which is the required equation of motion.

Explanation:

To derive the equation S=ut+1/2at^2 using integration method, we need to start with the basic equations of motion:

v = u + at (Equation 1)

S = ut + (1/2)at^2 (Equation 2)

We know that velocity, v is the derivative of displacement, S with respect to time, t i.e.,

v = dS/dt (Equation 3)

Using Equation 1, we can substitute v as (u + at) in Equation 3 and integrate both sides to get the value of displacement, S. The integration limits can be taken as initial time, t=0 and final time, t=t.

Integrating both sides of Equation 3, we get:

∫dS = ∫(u + at)dt

On integrating and applying the limits, we get:

S - 0 = ut + (1/2)at^2 - 0

Therefore, the final equation is:

S = ut + (1/2)at^2, which is the required equation of motion.

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