Homework Help: Questions about the formula for acceleration

1. Sep 25, 2014

Crovati

1. The problem statement, all variables and given/known data

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?

2. Sep 25, 2014

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.

Last edited: Sep 25, 2014
3. Sep 25, 2014

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

4. Sep 25, 2014

theOrange

Acceleration IS equal to distance/time2

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

The units for acceleration is: m/s2

5. Sep 25, 2014

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.