- #1
Ocata
- 198
- 5
Hello,Lets say I start off with constant acceleration of 1 m/s^2, and I want to evaluate it at 3 seconds.
a = 1.
a(3) = 1
then, since at=v,
v(t) = at = 1(3) = 3m/s then I can work backward v/t = a = 3/3 = 1
then, since vt = d
d(t) = vt = 3(3) = 9 then I can work backward d/t= v = 9m/3s = 3m/sThis way, the units make sense acceleration is 1 m/s/s
Take 9 meters. Divide it by 3 seconds. Then divide it again by 3 seconds. And voila, you arrive back at 1m/s/s
_______
However, if I integrate acceleration to get the kinematic equations, it all seems to fall apart and I don't know why.
[itex]\int a (dt) = at +v_0 = v_f[/itex] ,
so evaluating time = 3 with acceleration 1m/s^2,
v(3) = 1(3)+0 = 3m/s then I can work backward v/t = a = 3/3 = 1 => all good still
then
[itex]\int v (dt) = \frac{1}{2}at^2 +v_0(t)+r_0= r_f[/itex],
[itex]r(3) = \frac{1}{2}(1)3^2+0+0=4.5[/itex] so if I work backward this time d/t=v = 4.5/3= 1.5 m/s
But my velocity is 3m/s, not 1.5m/s
So my conclusion is, Distance/Time = Velocity will only hold true if there is 0 acceleration. Is this correct?
a = 1.
a(3) = 1
then, since at=v,
v(t) = at = 1(3) = 3m/s then I can work backward v/t = a = 3/3 = 1
then, since vt = d
d(t) = vt = 3(3) = 9 then I can work backward d/t= v = 9m/3s = 3m/sThis way, the units make sense acceleration is 1 m/s/s
Take 9 meters. Divide it by 3 seconds. Then divide it again by 3 seconds. And voila, you arrive back at 1m/s/s
_______
However, if I integrate acceleration to get the kinematic equations, it all seems to fall apart and I don't know why.
[itex]\int a (dt) = at +v_0 = v_f[/itex] ,
so evaluating time = 3 with acceleration 1m/s^2,
v(3) = 1(3)+0 = 3m/s then I can work backward v/t = a = 3/3 = 1 => all good still
then
[itex]\int v (dt) = \frac{1}{2}at^2 +v_0(t)+r_0= r_f[/itex],
[itex]r(3) = \frac{1}{2}(1)3^2+0+0=4.5[/itex] so if I work backward this time d/t=v = 4.5/3= 1.5 m/s
But my velocity is 3m/s, not 1.5m/s
So my conclusion is, Distance/Time = Velocity will only hold true if there is 0 acceleration. Is this correct?