Check the correctness-Sn - u -1 - 2 a 2 t -1

Here, S=u+(1/2)*a*(2n 1) this equation is used to find distance travelled by body in nth second. LHS So, S(nth) = distance travelled in nth second i.e S(nth) = ...

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Byju's Answer

Standard XII

Physics

Relating Circular Motion to SHM

Check the cor...

Question

Check the correctness
$s = u + \frac{1}{2} a (2 t - 1)$

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Solution

in order to check the correctness of the above equation we need to check if they are dimensionally correct , in simple terms if the units of L.H.S. quantities is same as units of R.H.S. quantities.
As it's given

$s = u + \frac{1}{2} a (2 t - 1)$
$t a k i n g t h e u s u a l m e a n i n g o f t h e a b o v e e q u a t i o n$
$s = d i s t a n c e o r d i s p l a c e m e n t (m e t e r) = [L]$
$u = s p e e d o r v e l o c i t y (\frac{m}{s e c}) = [L T^{- 1}]$
$a = a c c e l e r a t i o n (\frac{m}{s e c^{2}}) = [L T^{- 2}]$
$p u t a l l t h e u n i t s a s p e r g i v e n e q u a t i o n$
$[L] = [L T^{- 1}] + [L T^{- 2}] [T]$
$∴ L . H . S . i s n o t e q u a l s t o R . H . S .$

$∴theaboveequationisnotcorrectdimensionally\therefore the above equation is not correct dimensionally$

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Similar questions

Q. With the usual notations, check if the following equation

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

is dimensionally correct or not.

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

; make 't' the subject of formula.

Q. With the usual notations, the following equations

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

Q. Rewrite the following equation in terms of

t

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

Q. Check the correctness of the relation

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

, where

u

is initial velocity,

a

is acceleration and

S_{n t h}

is the distance travelled by the body in

n t h

second.

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Check the correctnesss=u+12a(2t−1)

Check the correctness
$s = u + \frac{1}{2} a (2 t - 1)$