Question

The velocity of a body is given by V=At2+BT+C if V and t are expressed in SI what are the unit of A B and C ?

Answer 1

Answer:

according to dimensional analysis, A+B is possible when their dimensions are same. so,

according to the equation,

the dimensions of thethree digits on right hand side would be same (separately) with left hand side. hence

[v]=LT^(-1)=AT^2

or,[A]= LT^(-3)

unit of A is m/s^(3)

in same way,

LT^(-1)=BT^(-1)

or,[B]= LT^(-2)

unit m/s^(2)

[C]=LT^(-1)

unit m/s

Answer 2

Answer:

here v=at²+bt+c

according to principle of homogeneity,

[v]=[at²]=[Bt]=[c] ; [v]=[at²]

Lt^-1=[a].T²⇒[A]=LT^-3

so, unit of   a is ms^-3

similarly

[v]=[bt]LT^-1=[B].T⇒[B]=LT-²

so unit of b is ms^-2

and [v]=[c]⇒[c]=LT^-1

so unit of c is ms^-1

Explanation:

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