Questions about the formula for acceleration

[Crovati]

Homework Statement

I know that acceleration = change in velocity/change in time. Wouldn’t acceleration therefore also = distance/time²?

I thought this was true until i learned the formula for motion
s=ut*1/2at²
where
s = distance and u = initial velocity

Here, if you re-arrange the formula (and assuming that initial velocity =0), a= 2s/t²

So which of these formulas are right?

And if i were to create a graph where the slope can help find the acceleration, should i graph 2*distance vs t² or just distance vs t²?

 

[haruspex]

Average acceleration is $\Delta v / \Delta t$, and average velocity is $\Delta s / \Delta t$. But $\Delta v$ is not average velocity, so you cannot combine those two equations.
The SUVAT formula you quote is only valid for constant acceleration.

 

[rcgldr]

Assume constant acceleration, using va for v average:

v1 = v0 + a Δt
va = 1/2 (v0 + v1)
s1 = s0 + va Δt = s0 + 1/2 (v0 + v1) Δt = s0 + 1/2 (v0 + (v0 + a Δt)) Δt = s0 + v0 Δt + 1/2 a Δt^2

 

[theOrange]

Homework Statement

I know that acceleration = change in velocity/change in time. Wouldn’t acceleration therefore also = distance/time²?

Acceleration IS equal to distance/time²

distance = meters (or m)
time = seconds (s)

The units for acceleration is: m/s²

 

[nasu]

No, the fact that is has the same units does not mean that they are the same.
Work is not torque even though both are measured in N*m.

Acceleration is a measure of change in speed. If the speed is constant, you have no acceleration even if there is some distance traveled in some time.