Quiz 0904
1. If
`ds stands for the displacement of an object and `dt for the time required then
among the following which can you determine from knowledge of `ds and `dt:
· vAve, vf, v0, `dv or a?
This is also our intuitive idea of velocity.
We can't find vf from just `ds and `dt. There are a lot of ways to travel 10 meters in 3 seconds (maybe have a running start and need to slow down, might start from rest and speed up, might start very fast and come to rest).
So there's no way to find vf of v0 (they could be anything), much less `dv or a.
Determine the value of each quantity that
can be determined.
2. If
you know v0, vf and `dt for a situation involving uniform acceleration which of
the following can you determine:
· vAve, `dv, `ds, a?
Since acceration is uniform we can average initial and final velocities to get average velocity:
vAve = (v0 + vf) / 2; again note this is the case only for unif accel.
Now we can multiply vAve by `dt to get `ds (we know to do this from basic intuition; also since vAve = `ds / `dt we can solve for `ds to get `ds = vAve * `dt.
The result of the process of finding `ds is thus
`ds = vAve `dt = (vf + v0) / 2 * `dt.
This is the First Equation of
Uniformly Accelerated Motion: `ds = (vf + v0) / 2 * `dt.
`dv is the change in velocity. We get change in velocity by subtracting initial velocity from final velocity: `dv = vf - v0. So we can get `dv from the given information.
Acceleration is rate of change of velocity. Average rate of velocity change is aAve = `dv / `dt.
Since acceleration is uniform it's always the same as average acceleration so we can just say a = `dv / `dt.
In terms of the original quantities vf, v0 and `dt this reads
a = (vf - v0) / `dt.
This is the Second Equation of Uniformly Accelerated Motion.
The Second Equation of Uniformly Accelerated Motion is often algebraically rearranged to the form
vf = v0 + a `dt (usual form of Second Equation of Uniformly Accelerated Motion).
Determine the value of each quantity that
can be determined.
3. If
you know v0, vf and `dt for a situation involving nonuniform acceleration which
of the following can you determine:
·
vAve, `dv, `ds, a?
vAve = `ds / `dt, always. We might be tempted to say that vAve = (vf + 0) / 2, the average of initial and final velocities, but this assumes a straight-line v vs. t graph. Acceleration isn't uniform in the given situation. So we can't use vf and v0 to find vAve. Nothing given in this situation will give us vAve since acceleration isn't uniform.
`dv = vf - v0, so we can find `dv.
We also know that aAve = `dv / `dt, so we can find aAve. However we don't know any specific acceleration, since accel is nonuniform, so we can't determine a value of the acceleration a. We can only find average acceleration.
Determine the value of each quantity that
can be determined.
4. If
you have an accurate graph of v vs. t over a definite time interval which of the
following can you determine (do not assume uniform acceleration):
·
v0, vf, initial acceleration, final acceleration, average
acceleration, `ds?
Explain how you can determine each of these quantities.
A graph of v vs. t will tell you initial and final velocity. Knowing the time interval `dt you can then find average acceleration `dv / `dt, which is the rise / run = average slope of the graph.
Acceleration is represented by the slope of the graph. If you can draw good tangent lines to the graph you can find their slopes, which will represent initial and final velocities.