Question

With the usual notations, the following equation

$S_{t} = u + \frac{1}{2}a(2t - 1)$ is

• A. Only numerically correct
• B. Only dimensionally correct
• C. Both numerically and dimensionally correct
• D. Neither numerically nor dimensionally correct

Answer 1

Answer: (C)

Both numerically and dimensionally correct

Answer 2

Given $S_{t}$= distance travelled by the body in t^th sec.= $\lbrack LT^{- 1}\rbrack$, a = Acceleration = $\lbrack LT^{- 2}\rbrack$,

v = velocity = $\lbrack LT^{- 1}\rbrack$, t = time = [T]

By substituting the dimension of each quantity we can check the accuracy of the formula

$S_{t} = u + \frac{1}{2}a(2t - 1)$

$\therefore\lbrack LT^{- 1}\rbrack = \lbrack LT^{- 1}\rbrack + \lbrack LT^{- 2}\rbrack\lbrack T\rbrack$ ⇒

$\lbrack LT^{- 1}\rbrack = \lbrack LT^{- 1}\rbrack + \lbrack LT^{- 1}\rbrack$

Since the dimension of each terms are equal therefore this equation is dimensionally correct. And after deriving this equation from Kinematics we can also proof that this equation is correct numerically also.