the distance covered by a particle in time is given by x=a+bt+ct2+dt3 find the dimensions of a, b, c, d
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Solution :-
We have got the expression of distance x
x = a + bt + ct² + dt³
And question asked is to find out the dimensions of a , b , c and d .
Now first let us consider these dimensions :-
▪️Dimension of length = L
▪️Dimension of time = T
▪️Dimension of mass = M
Now we will consider the distance
Dimension of Distance
= M⁰ L¹ T⁰
So the Dimensions of a , b , c and d must be resulting in the Same form.
Dimension of "a"
As no other quantity is multiplied/divided with it .
So dimension of a = M⁰ L¹ T⁰
Dimension of "b"
As "t" is multiplied with it
So dimension of b = M⁰ L¹ T⁻¹
Dimension of "c"
As t² is multiplied with it
So dimension of c = M⁰ L¹ T⁻²
Dimension of "d"
As t³ is multiplied with it
So dimension of d = M⁰ L¹ T⁻³
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