Question

1-5 Dimensional analysis is a powerful way to check the results of a physics calculation 41. One equation that describes motion of an object is where x is the position of the object, a is the acceleration, t is time, vo is the initial speed, and xo is the initial position. Show that the dimensions in the equation are consistent.

Answer 1

The dimension of position is 'L'

The dimension of velocity is 'L/T'

The dimension of acceleration is 'L/(T^2)'

from this we can show that the equation is dimensionaly consistent

here i attach an image for better understanding

The dimension of position is 'L' The dimension of velocity is 'L/T' The dimension of acceleration is 'L/(T^2)' from this we can show that the equation is dimensionaly consistent here i attach an image for better understanding x = 1/2 at^2 + v_0t + x_0 x rightarrow position of the object dimension of x is 'L' V_0 rightarrow initial velocity (speed) V_0 = x_0/t = LT^-1[dimension] X_0 rightarrow initial position Dimension of X_0 rightarrow l and 'a' is the acceleration: a = u_0/t = x_0/t^2 dimention = LT^-2 so, the dimensions in the equation [L] = [LT^-2 T^2] + [LT^-1 T] + [L] therefore [L] = [L] + [L] + [L]