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The velocity of a body is given by v=At^...

The velocity of a body is given by `v=At^2+Bt+C`. If v and t are expressed in SI, what are the units of A,B and C?

Text Solution

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From principle of Homogeneity the terms `At^2`, Bt and C must have same dimensional formula of velocity `v`.
`v=velocity=LT^-1impliesLT^-1=A[T^2]`
`thereforeA=(LT^-1)/T^2=LT^-3.` So unit of A is `m//sec^3`
`LT^-1=BTimpliesB=LT^-2` So unit of B is `m//sec^2`
`LT^-1=C` So unit of C is `m//sec`
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