Delivation of v=u+at in physics?

Question

Delivation of v=u+at in physics?

Answer 1

So I think you might be asking Derivation of v = u + at

I'm not sure what u represents but it must be some sort of velocity term so I think you mean this

Vf = Vi + at

This equation only works at constant acceleration or if you are given the average acceleration OR if you calculate the average acceleration by (af + ai)/2. (af + ai)/2 only works when the super acceleration is constant (super acceleration is the change in acceleration).

Really all the equation says is:

Change in V = (average a)*t

There are way to derived it through calculus which requires differentiating position. Really though, the equation is pretty intuitive as is.

Answer 2

assume,

u=initial velocity

v= final velocity

then the acceleration of the body in the time t is given by

         a=(v-u)/t

         v-u=at

         v=u+at

Answer 3

according to definition of acceleration,

acceleration=rate of change of velocity per unit time

therefore

a=dv/dt

or

dv=a.dt

now integrating on both sides from velocity u to v and time 0 to t

v-u=at

or v =u+at

Answer 4

Hi,

It's actually an integral. You may not have done them yet ...you will near the end of high school most likely.

Let s(t) represent the displacement of a particle at time t.

Then ds/dt is the velocity v(t) (ds/dt is a rate of change ...if s were a linear or straight line graph ds/dt would just be the slope ...if s(t) were a curve, then ds/dt at a point t_0 would represent the slope of a tangent line at t_0 or the velocity of the particle at t=t_0)

The acceleration of the particle (actually the vector component along an axis of your choice) ...is d^2s/dt^2=a(t)

Think of it as the slope of the velocity graph ....

now integrating a(t)dt

we get v(t) = A(t)+C

so if a(t) were constant call it a

then v(t) = at +C where C is the initial velocity and a is the constant accleration ...that comes from integrating

INTEGRAL[ a*dt] =at+C =v(t)

check the units too ...and you can see a is in m/s^2

so m/s^2 * s = m/s

and C is in m/s so it works out

I hope it helps