Is this equation involving the acceleration of gravity correct?

Huzaifa
Homework Statement:
Is this equation correct: $$g=\dfrac{v}{t}=\dfrac{2s}{t^{2}}=\dfrac{2\left( vt-s\right) }{t^{2}}=\dfrac{v^{2}}{2s}=9.8ms^{-2}$$?
Relevant Equations:
##g=\dfrac{v}{t}=\dfrac{2s}{t^{2}}=\dfrac{2\left( vt-s\right) }{t^{2}}=\dfrac{v^{2}}{2s}=9.8ms^{-2}##
\begin{aligned}v=u+at\\ \Rightarrow v=gt\\ \Rightarrow g=\dfrac{v}{t} \cdots (1)\end{aligned}
\begin{aligned}s=ut+\dfrac{1}{2}at^{2}\\ \Rightarrow s=\dfrac{1}{2}gt^{2}\\ \Rightarrow g=\dfrac{2s}{t^{2}}\cdots (2)\end{aligned}
\begin{aligned}s=vt-\dfrac{1}{2}at^{2}\\ \Rightarrow s-vt=-\dfrac{1}{2}at^{2}\\ \Rightarrow g=\dfrac{2\left( vt-s\right) }{t^{2}} \cdots (3)\end{aligned}
\begin{aligned}v^{2}-u^{2}=2as\\ \Rightarrow v^{2}=2as\\ \Rightarrow g=\dfrac{v^{2}}{2s} \cdots (4)\end{aligned}
$$g=\dfrac{v}{t}=\dfrac{2s}{t^{2}}=\dfrac{2\left( vt-s\right) }{t^{2}}=\dfrac{v^{2}}{2s}=9.8\ \mathrm{m s^{-2}}$$

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What's the question precisely?

Steve4Physics
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Homework Statement:: Is this equation correct: $$g=\dfrac{v}{t}=\dfrac{2s}{t^{2}}=\dfrac{2\left( vt-s\right) }{t^{2}}=\dfrac{v^{2}}{2s}=9.8ms^{-2}$$?
Relevant Equations:: ##g=\dfrac{v}{t}=\dfrac{2s}{t^{2}}=\dfrac{2\left( vt-s\right) }{t^{2}}=\dfrac{v^{2}}{2s}=9.8ms^{-2}##

\begin{aligned}v=u+at\\ \Rightarrow v=gt\\ \Rightarrow g=\dfrac{v}{t} \cdots (1)\end{aligned}
\begin{aligned}s=ut+\dfrac{1}{2}at^{2}\\ \Rightarrow s=\dfrac{1}{2}gt^{2}\\ \Rightarrow g=\dfrac{2s}{t^{2}}\cdots (2)\end{aligned}
\begin{aligned}s=vt-\dfrac{1}{2}at^{2}\\ \Rightarrow s-vt=-\dfrac{1}{2}at^{2}\\ \Rightarrow g=\dfrac{2\left( vt-s\right) }{t^{2}} \cdots (3)\end{aligned}
\begin{aligned}v^{2}-u^{2}=2as\\ \Rightarrow v^{2}=2as\\ \Rightarrow g=\dfrac{v^{2}}{2s} \cdots (4)\end{aligned}
$$g=\dfrac{v}{t}=\dfrac{2s}{t^{2}}=\dfrac{2\left( vt-s\right) }{t^{2}}=\dfrac{v^{2}}{2s}=9.8\ \mathrm{m s^{-2}}$$
What you have is multiple equations.

You need to describe the overall situation. Also define precisely what each variable means.

Steve4Physics
Huzaifa
You need to describe the overall situation. Also define precisely what each variable means.
The overall situation is constant or uniform acceleration. Here, s = displacement, u = initial velocity, v = final velocity, a = acceleration, t = time. These are equations of motion.

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None of the numbered equations [except maybe (3)] are generally true.
Each is true in some special [so far unstated] cases

Steve4Physics
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Hi @Huzaifa. You seem to be making a number of unstated assunptions, e.g.
- motion is in the vertical direction only, with gravity the only force;
- initial velocity (u) is zero, so you are only considering objects released from rest at t=0.

But of course I'm just guessing, as you haven't yet answered @PeroK's question (Post #2).

SammyS