Four equations for gravitational acceleration from kinematic formulas

[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

$g=\dfrac{v}{t}=\dfrac{2s}{t^{2}}=\dfrac{2\left( vt-s\right) }{t^{2}}=\dfrac{v^{2}}{2s}=9.8ms^{-2}$

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

 

[PeroK]

What's the question precisely?

 

[SammyS]

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.

Of course, answer the question asked by @PeroK. .

 

[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.

 

[robphy]

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

 

[Steve4Physics]

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).