Effect of Direction

In class, we had a VERY long, in depth conversation about the effect that direction has on measurements. 

1) Distance & Position

• distance - measurement of total length traveled
• position - displacement from reference point in a certain direction
• displacement - length between starting point and ending point

Unlike distance, position is effected by direction. Distance is also the total length traveled that includes if one travels backward.

Ex) a cyclist rides his bike for four miles, rides back one mile, and then turns back around and continues in the original direction for three miles.

Distance = 4 + 1 + 3 = 8

Position = 4 - 1 +3 = 6

*Distance and displacement are also measured starting at the starting point; while, position always refers to the reference point.

2) Speed & Velocity

• speed - distance/time
• velocity - position(distance+direction)/time

*Speed is the slope of a distance vs. time graph; while velocity is the slope of a position vs. time graph.

Also, the formula for position is...

x    =    v    •    t  ±  x₀

^position ^velocity ^time ^starting position

Buggy Lab

I thought this was kind of a weird lab because we got some odd results for our second scenario.

In the first scenario, we started the buggy car at the reference point and counted how many centimeters for every 5 seconds that the buggy car ran.

This first scenario was pretty easy. Our results gave us a direct, linear graph.

Although in the second scenario, we moved our buggy car back 40 cm behind the reference point. We still counted how many centimeters away from the reference point for every 5 seconds that the buggy car ran.

This is where the results get funky. Our graph is like an absolute value. My group decided on this graph because a position cannot be a negative distance away from the reference point. So for those who don’t know, the graph would look kind of like a linear line and then flipping the negative half of the line over the x-axis to make a “V” shape.

In our graphs, the x-axis was the reference point. Whether at the origin or somewhere along the x-axis, that point where the line touches the x-axis always represents the reference point.  

Converting: English Style

Last time I talked about converting between metric units. This was pretty easy for me (even using powers of 10).

Although this time, I’ll be talking about converting between English units. My friend showed me this little trick on remembering the conversion rate between gallons and cups. It’s called the Gallon Man.

Ain’t it cute!

Anyway, the reason that conversions between English units are harder is because the conversion factors are not standardized and are very random. So, converting between English units takes a longer process than just multiplying and dividing by 10. The easiest way to convert is cross cancellation of units.

Ex)  1m│100cm = 100cm

        1   │ 1m            1

m → cm

The two m (meter) are cancelled out because m/m=1.

Let’s try one a little more complicated

Ex) 200cm│   1m     │  1km  │ 60sec │60min =  720,000km = 72km =   72km/hr

         1sec │ 100cm │ 100m│ 1 min   │1 hr          10,000 hr       1hr

This conversion shows cm/sec → km/hr

Cross cancellation works by multiplying all the top numbers together then dividing it by the product of all the bottom numbers.