the first equation, v(t) = v0 + a t describes correctly how to find the velocity of an object if you know its initial velocity, v0, its acceleration, a, and the time of travel t
as in: a car starts at 20m/s and then accelerates at the rate of 3m/s/s for ten seconds; what is its speed at the end of the ten secs
v(10)=20m/s + 3m/s/s x 10s = 50m/s
the second equation is incorrect; I believe you are looking for
dist = v0 t + 1/2 a t^2
this tells you how far an object travels in a certain time if you know its initial velocity and acceleration
so the car above would travel a distance
dist = 20m/s x 10s + 1/2 x 3m/s/s x (10s)^2 = 350m while it is accelerating
as in: a car starts at 20m/s and then accelerates at the rate of 3m/s/s for ten seconds; what is its speed at the end of the ten secs
v(10)=20m/s + 3m/s/s x 10s = 50m/s
the second equation is incorrect; I believe you are looking for
dist = v0 t + 1/2 a t^2
this tells you how far an object travels in a certain time if you know its initial velocity and acceleration
so the car above would travel a distance
dist = 20m/s x 10s + 1/2 x 3m/s/s x (10s)^2 = 350m while it is accelerating
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OK, lynx, you need to learn something about units analysis.
v, for velocity or speed, has length per time units. In kms SI units, that's meters per second (m/s).
That means the RHS of both equations must result in m/s units. And there's your first clue as to "which one...to use." Check the units.
On the first equation you have v + at; so you have m/s in the first teim and m/s^2*sec ~ m/s in the second term. So the RHS does in fact result in m/s units. So that's probably a good equation to use to find velocity.
Now what about the second one?
You have v + 1/2 at^2; so the first term units are m/s and that's good when we're looking for m/s in the answer. But what about the second term?
That's clearly m/s^2 * s^2 ~ m. And look here, the second term is not in m/s; it's in meters only...length.
So clearly the second equation is incorrect for finding speed. It has the wrong units in the RHS. And that, lynx, is how you test for what equation to use.
v, for velocity or speed, has length per time units. In kms SI units, that's meters per second (m/s).
That means the RHS of both equations must result in m/s units. And there's your first clue as to "which one...to use." Check the units.
On the first equation you have v + at; so you have m/s in the first teim and m/s^2*sec ~ m/s in the second term. So the RHS does in fact result in m/s units. So that's probably a good equation to use to find velocity.
Now what about the second one?
You have v + 1/2 at^2; so the first term units are m/s and that's good when we're looking for m/s in the answer. But what about the second term?
That's clearly m/s^2 * s^2 ~ m. And look here, the second term is not in m/s; it's in meters only...length.
So clearly the second equation is incorrect for finding speed. It has the wrong units in the RHS. And that, lynx, is how you test for what equation to use.