The equation for the change of position of a train starting at x=0 m is given by x=(1)/(2)at^2+bt^3 . The dimensions of b are: a) T^-3 b) LT^-3 C LT^-2 D LT^-1 E L^-1T^-1

Question

Answer 1

The correct answer is:b)

Explanation:The equation for the change of position of the train is given by

, where

represents the position,

is a constant,

is the time, and

is the coefficient we need to find the dimensions for.To find the dimensions of

, we need to analyze the dimensions of each term in the equation.The dimensions of

are

(length), and the dimensions of

are

(time).The dimensions of the first term,

, are

(since

is dimensionless and

has dimensions of

).The dimensions of the second term,

, are also

(since

has dimensions of

and

has dimensions of

).Since the dimensions of both terms are the same (

), we can equate the dimensions of the coefficients:

Therefore, the dimensions of

are

.

Soru