Question

if y=a+bt +ct^2 where y is the distance and t is time what is the dimension and unit of c?

Answer 1

Answer:

Explanation:

given expression, y = a + bt + ct²

where y is the distance and t is the time.

we know,

dimension of time, t = [T]

dimension of distance, y = [L]

from dimensional analysis,

dimension of y = dimension of a = dimension of bt = dimension of ct²

case1 : dimension of y = dimension of a

so, dimension of a = [L]

case 2 : dimension of y = dimension of bt

or, dimension of b × dimension of t = [L]

or, dimension of b × [T] = [L]

so, dimension of b = [LT-¹]

case 3 : dimension of y = dimension of ct²

or, dimension of c × dimension of t² = [L]

or, dimension of c × [T]² = [L]

so, dimension of c = [LT-²]

Answer 2

Answer:

y=distance=[L]

T=time=[T]

as we know,

y=a, y=bt,y=ct^2

so,

(i). dimension of y=dimension of a

or,  [L]=a

therefore, dimension of a =[L]

(ii). dimension of bt=dimension of y

or, dimension of b*[T]= [L]

therefore dimension of b=[LT^-1]

(iii). dimension of ct^2=dimension of y

or, dimension of c*dimension of t^2=[L]

or, dimension of c* [t^-2]=[L]

therefore, dimension of c=[Lt^-2]

hence, unit of c= m/s^2

Explanation: