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The distance d that a certain particle moves may be calculated from the expression d = at + bt2 where a and b are constants; and t is the elapsed time. what must the dimensions of the quantities a and b be, respectively?

User Tasegula
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1 Answer

5 votes
Guven that the distance d that a certain particle moves may be calculated from the expression
d = at + bt^2 where a and b are constants; and t is the elapsed time.

Distance is a length and hence the dimension of distance is L.

Now,
at and
bt^2 also will have the dimension of L.

Time has a dimension of T.

For
at, let the dimension of
a be
X, then

XT=L \\ \\ \Rightarrow X=(L)/(T)

For
bt^2, let the dimension of
b be
Y, then

YT^2=L \\ \\ \Rightarrow Y= (L)/(T^2)

Therefore, the dimension of
a is
(L)/(T) while the dimension of
b is
(L)/(T^2).
User Apieceofbart
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