phy201
I am having some trouble checking my units, can you help me?
Also when answering my last question about the physics quiz, you said see my notes for a couple of corrections, does that just mean that days notes?
An object is given an known inital velocity up a long ramp on whcih its acceleration is known to have magnitude 6cm/s^2.223 seconds later it passes for the first time a point 5cm up the ramp from its inital positionI can solve the initial velocity and the final velocity, but then it asks how long will it be before it passes this point again?I'm not sure on how to answer this one.
An example of checking your units:
Recall that for fractions:
(a / b) * (c / d) = (a * d) / ( b * d)
(a / b) / (c / d) = (a / b) * (d / c): division by a fraction is the same as multiplication by its reciprocal.
( a * b) / b = a * ( b / b) = a, since b / b = 1.
Like most mathematics, these rules make more sense if you write them out on your paper than if you try to read them in typed notation.
For the equation `ds = v0 `dt + .5 a `dt^2 we know that
`ds has MKS units of m
v0 has MKS units of m/2
`dt has MKS units of s
a has MKS units of m/s^2.
The units of the left-hand side have to match the units of the right-hand side.
The units of both of the terms v0 `dt and .5 a `dt^2 on the right-hand side have to match so the quantities can be added.
The unit of the left-hand side is just the unit of `ds, which is m.
The unit of v0 * `dt is (m/s) * s = (m/s) * (s/1) = m * s / ( s) = m * ( s / s) = m.
The unit of .5 a `dt^2 is (m / s^2) * (s)^2 = (m / s^2) * ( s^2 / 1) = (m * s^2) / s^2 = m * (s^2 / s^2) = m.
So the units of both v0 `dt and .5 a `dt^s are m.
Thus the unit of the right-hand side is m.
The units of the left- and right-hand sides are both m, and the units therefore check out.