Question

show dimensional s=vt+1/2at^2

Answer 1

Here is the derivation of the equations of motion by graphical method. Follow the graph:

Let us suppose that v is the initial velocity of the particle, at time t = 0, and v be the velocity of the particle at t = t.  

The acceleration a of the particle can be written as

refer image 1

This is the 1 kinematic equations for uniformly accelerated motion.

Suppose, the particle travels a distance x in the time t .

refer img 2

The area of blue colored part gives the distance covered x .

So,

reffer img 3

reffer image 4

Answer 2

DIMENSION :-

A phenomena in which all physical quantities are converted into base quantities . i.e , mass ,time,length and then represent these quantities interms of M , L , T .

Dimensions of s=vt+ 1/2 at^2 :-

v is velocity its unit is :- ms^_1

a is acceleration its unit is ms^_2

t is time its unit is 'sec'

Put these units to the above equation

s= ms^_1 .s +ms^_2. t^2 ------------------------(1)

Length as [L] ---------------- (a)

Time as [T] ------------ (b)

Put a , b , c in place of units in equation 1

s = LT^_1 .T + LT^_2 .T^2 (T^_2 cancels T^+2 , T^_1 cancels T)

s = L + L

s = [ L]

So

Dimension of s=vt+1/2at^2 is [L]


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