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omeli [17]
3 years ago
9

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?
Mathematics
1 answer:
pychu [463]3 years ago
4 0
Guven that the <span>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.

</span><span>Time has a dimension of T.

For at, let the dimension of a be X, then
XT=L \\  \\ \Rightarrow X=\frac{L}{T}

For bt^2, let the dimension of b be Y, then
YT^2=L \\  \\ \Rightarrow Y= \frac{L}{T^2}

Therefore, the dimension of a is \frac{L}{T} while the dimension of b is \frac{L}{T^2}.
</span>
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