Mathematics, 05.09.2019 20:10 jorge0506
(a) assume the equation x = at3 + bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. determine the dimensions of the constants a and b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.)
Answers: 3
![[x]=[A][t]^3+[B][t]](/tpl/images/0223/7049/64b45.png)
![[x]=L](/tpl/images/0223/7049/c94b9.png)
and t has a time dimension, ![[t] = T](/tpl/images/0223/7049/a7745.png)
, so we get![L = [A]T^3+[B]T](/tpl/images/0223/7049/85048.png)
![[A]T^3=L](/tpl/images/0223/7049/0d3d9.png)
![[B]T=L](/tpl/images/0223/7049/a577d.png)
![[A]T^3=L\\](/tpl/images/0223/7049/fa4a2.png)
![\boxed{[A] = \cfrac{L}{T^3}}](/tpl/images/0223/7049/2d879.png)
![\boxed{[B]=\cfrac LT}](/tpl/images/0223/7049/ef266.png)
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(a) assume the equation x = at3 + bt describes the motion of a particular object, with x having the...
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