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Question

The velocity v of a particle at time t is given by v=at+bt+c, where a,b and c are constants.The dimensions of a,b and c are respectively:

A
LT2, L and T
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B
L2, T and LT2
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C
LT2, LT and L
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D
L, LT and T2
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Solution

The correct option is A LT2, L and T
Two terms can be added or subtracted if their dimensions are same.
Thus c has the dimension of time i.e. [T]
Dimension of v and at must be same.
Thus dimensions of [a]=[v][t]=[LT1][T]=[LT2]
Dimensions [b]=[v][t]=[LT1][T]=L

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