Question

Derive the equation of motion by graphical method - s = ut + 1/2 at 2 .

Answer 1

Answer:

Explanation:

here are mostly two types of graphs that are used for analysing the kinematical behavior of different bodies, namely s-t graph also called displacement time graph and the other one is v-t graph also called the velocity time graph. By the term 'kinematical behavior’ I mean the nature of the type of motion of the body and other important calculations like it's speed or velocity, acceleration, retardation and things related to its motion or rest.

The slopes of these two graphs provide two different yet very important data. The slope of v-t graph gives acceleration where as the slope of s-t graph gives velocity.

Now I won't spend much time on s-t graph because that's not my point of interest. So I will straight move to my point i.e v-t graph.

Now how does a v-t graph of a body having some initial velocity say u moving with a uniform velocity look like? It's like this



So the curve here is a trapezium ,the area of which is given by  (sum of parallel sides)*height.

Here that area is equal to s i.e displacement because area under the curve of a v-t graph gives displacement.

So from the diagram

Area=  

 

Now you know that 

So replacing v by the above relation in the equation of area we get,

 

So we get 

I have sufficiently help you out.