Question

SHOW THAT S=UT +1BY2 AT2

Answer 1

What is the derivation of motion of s=ut+1/2at^2?

The symbols:

t is time

s is the distance travelled at time t

u is initial velocity at t=0

a is acceleration which is constant

The distance is the area under the velocity line in the velocity/time graph.

Normally we would have to use calculus to calculate this. But if the acceleration is constant then the graph is a straight line and we can use geometry to calculate the area instead.

Here’s a picture of a velocity time graph with constant acceleration.

The distance travelled is the light blue area under the blue velocity line.

The velocity starts at initial value u and increases with acceleration a for time t w...

Let;

d=distance

S=speed

t=time

s=displacement

v=velocity

So now;

S=dt

If we use velocity instead of speed…then the distance becomes displacement instead of distance hence;

v=st

s=v∗t

But obviously we will be using average velocity since velocity might not be constant throughout.

s=v+u2∗t

Now let's look at another equation;

a=v−ut, where a is acceleration, v is final velocity, u is until velocity and t is time taken

Rearranging this equation we get;

v=u+at

We substitute this value of v is the first equation we got;

s=u+at+u2∗t

s=2ut+at22

s=2ut2+at22

s=ut+12at2

Hope I helped

Sivapriyaa ‍♀️