course Mth163

I am really confused with this problem and I am not sure if I approached this correctly. I reviewed the notes and the basic quantities/relationship file but I'm still unsure. I believe the .9 has thrown me off and I'm not comprehending the right. Can you help me?

"An automobile traveling a straight line is at point A at clock time t = 9 sec, where it is traveling at 10 m/s, to a certain point B. If the automobile accelerates uniformly at a rate of .9 m/s/s, then if it reaches point B at clock time t = 14 sec, what is its velocity at that point? What is its average velocity over the interval from A to B? If at point A the automobile is 44 meters from the starting point, how far is point B from the starting point?

The automobile is at 44 meters at 9 seconds, when the car reaches point B, it will be at 48.5m (.9m/s/s * 5s). The velocity at point B will be 14.5m/s (10m/s + 4.5m/s), the average velocity will be 12.25m/s (14.5 – 10 = 4.5/2).

Hopefully the following will be helpful:

This problem is related to motion on an interval.

To start any such problem you need to identify your information.

Motion is analyzed in terms of the following quantities:

clock time

position

velocity

acceleration

Each of these quantities has a value at the beginning of the interval, a value at the end of the interval, and an average value (and/or perhaps a midpoint value) during the interval.

The value of a quantity at the beginning of an interval will generally be referred to as the 'initial' value of that quantity.

The value of a quantity at the end of an interval will generally be referred to as the 'final' value of that quantity.

The average value of a quantity on an interval will generally be referred to as the 'average' value of that quantity.

The change in a quantity on an interval is the difference between its initial and its final value.

So the quantities of interest will usually consist of some combination of the following:

initial clock time, often denoted t0

final clock time, often denoted tf

midpoint clock time, often denoted t_mid

change in clock time, often denoted `dt and equal to tf - t0

initial position, often denoted x0 or s0

final position, often denoted xf or sf

(midpoint position), not usually and important quantity and with no standard symbol

change in position, often denoted `dx or `ds and equal to xf - x0 or sf - s0

initial velocity, often denoted v0

final velocity, often denoted vf

average velocity, often denoted vAve

change in velocity, often denoted `dv and equal to vf - v0

initial acceleration

final acceleration

average acceleration

change in acceleration

When considering uniformly accelerated motion, the initial, final and average accelerations are all the same, and the change in acceleration is zero. When this is the case we just use the letter a to refer to 'the acceleration', understanding that a refers to initial, final and average acceleration all at once.

We are typically given at least a few of the initial and/or final and/or average and/or changes in the values of some of these quantities. If we are given a sufficient number of values, we can determine a number of other values.

To begin analyzing motion on an interval it's often a good strategy to identify the interval, the quantities for which we are given or can easily determine values, and the quantities we are trying to find.

A list of quantities to identify, if possible:

t0

tf

`dt

s0

sf

`ds

v0

vf

vAve

`dv

a

For the present problem, take this list and identify which quantities you are given, and which quantities you think you need to find.

Submit a copy of this document and insert the values of the given quantities next to their symbols.

Make note of the quantities think the problem asks you to find.

Make your best attempt to then reason out new information from the given information.

I'll respond by asking the additional questions I believe will help lead you toward the solutions you are seeking.