Question

Using calculus method ,derive s=ut+1÷2AT×2​

Answer 1

We know that s=ut +1/2at² , here t = time,

u = initial velocity, a = acceleration and s=displacement.

Taking the first derivative with respect to time:

ds/dt=d(ut+1/2 at²) /dt

ds/dt is the rate of change of displacement with respect to time , known as velocity.

And v=u+at ,

Take second derivative:

d²s/dt²= dv /dt =d(u+at)/ dt = a

d²s/dt² is the rate of change of velocity with respect to time, which is known as acceleration.