Question

If y=a+bt+ct^2 where y is the distance and t is the time. What is the dimension and unit of c

Answer 1

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:

if y =a+by+ct^2

Explanation:

by the principle of homogeneity

now,

or y=ct^2

or. c=y/t^2

or. c=[L]/[T^2]

or. c= [M^0LT^-2]