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In the equation of motion, $x = at + b t^{2}$ , the units of $a$ and $b$ are

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m / s^{2}, m / s

m / s, m / s^{2}

m / s, m / s

None of these

answer is B.

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Detailed Solution

In the equation of motion,

x = at + b t^{2}

, the units of a and b are

m / s

and

m / s^{2}

, respectively.
When each term has the same dimension on both sides of the equation, an equation is said to be dimensionally correct by the homogeneity of dimension principle.
Thus,

[x] = [at]

⇒

[x] = [b t^{2}]

⇒

[a] = [\frac{x}{t}]

⇒

[b] = [\frac{x}{t^{2}}]

Given that both

x

and

t

have length dimensions, the units of

a

and

b

will be in

m / s

and

m / s^{2}

, respectively.

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