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

1. [L², T and LT²]
2. [LT², LT and L]
3. [L, LT and T²]
4. [LT², T and L]

Correct answer: [LT², LT and L]

Solution

The term 'at' has the same dimensions as velocity, so the dimension of 'a' is [LT⁻²]. The term 'b/(t + c)' also has the same dimensions as velocity, so 'b' has dimensions [LT]. Since 't' and 'c' are added, they must have the same dimensions, which is [T].

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