Question

Distance covered by particle time is give by x= a+ bt +ct2+ dt3. Find diamension a,b,c,d

Answer 1

Answer:

Taje x = L (distance ) and t = T ( time)

Explanation:. given : x = a +bt+ct2+dt3

So, a = x = L ;. x = bt ; so, b = (x /t ) ;. So, b = LT ^-1 ; c = ( x /t2); c = LT^-2 means LT power( - 2) and similarly , . d = LT power( - 3)

Answer 2

Explanation:

Given =a+bt+ct^2+dt^3

In above given equation there are five dimension a,b,c,d,t

All of the term must have the same dimension of length to give final dimension ([x])in length .

Therefore ([x])=L

also, [bt]=L

b=L/T

b=LT^-1

also , [ct^2]=L

ct=L/T^2

ct=LT^-2

now, [dt^3]=L

dt=L/T^3

dt=LT^-3

Hence value of a=L, b=LT ^-1, c=LT^-2, d=LT^-3