Question

derive the equation the relation between displacement and time ​

Answer 1

Answer:

please write your question clearly so other students can answer your question. : )

Answer 2

SoluTion:

We know that, velocity is given by rate of change of position with respect to time.

v = dx/dt

→ vdt = dx

Here, v is not independent of time. So we'll use first equation of motion and replace v to u + at.

→ (u + at)dt = dx

Integrating LHS and RHS, from limits zero to t and xo to x respectively.

→ $u \displaystyle \int\limits_{0}^{t} dt + a \displaystyle\int\limits_{0}^{t} tdt = \displaystyle\int\limits_{x_o}^{x} dx$

→ ut + 1/2 at² = (x - xo)

Hence, our required expression is :

→ $\large{\boxed{\sf{x = x_{o} + ut + \dfrac{1}{2} at^{2}}}}$