The Big 5 KINEMATIC EQUATIONS

Formula 1:


This formula comes directly from the graph.
To find acceleration on a v -> t graph, you find the slope.

a = rise/run
a = ∆v / ∆t
a = (v2 - v1) / ∆t
a∆t = v2 - v1


Formula 2:


To find d on a v-> t graph, you find the area.

Area of a trapezoid: A = (a+b)h /2
d = (v1 + v2)∆t / 2
2d= (v1 + v2)∆t d = 1/2(v1 + v2)∆t


 Formula 3:


A and d must be included because they were already proven.

From Formula (1), isolate v2.v2 = a∆t + v1 =☺
Sub ☺ into Formula (2).
d = 1/2(v1 + ☺)∆t
d = 1/2(v1 + a∆t + v1)∆t
d = 1/2∆t(2v1 + 2∆t)d = v1∆t + 1/2a∆t²

Formula 4:


From Formula (1), isolate v1.v1 = a∆t - v2 =☻
d = 1/2(☻+ v2)∆t
d = 1/2(-a∆t + v2 + v2)∆t
d = 1/2∆t(-a∆t +2v2)
d = v2∆t - 1/2a∆t²

Formula 5:


Isolate ∆t from Formula 1.
a∆t = v2-v1
∆t = v2 - v1/a = A
sub A into Formula (2).
d = 1/2(v1 + v2)(v2 - v1/a)
ad = 1/2(v2 + v1)(v2 - v1)
2ad = v2² - v1²v2² = v1² + 2ad

There is another method of doing Formula 5, but I prefer this method.

Motion Sensor Graphs

D-t Graphs

This stimulation helps with understanding the displacement, velocity and acceleration graphs.

 Click here, it's fun :)

In a d-t graph, if you are walking at a constant rate away, then the line would slope upward away from the origin. If you walk at a constant rate forward, then the line would slope downward away from the origin. If the line is horizontal, there is no movement at that particular point.


A. Stand 1 m away from the origin, and stay for 1 second.

B. Walk 1.5 m away from the origin for 2 seconds.

C. Stand 2.5 m away from the origin, and stay for 3 seconds.
D. Walk 0.75 m toward the origin for 1.5 seconds.
E. Stand 1.75 m away from the origin, and stay for 2.5 seconds.

A. Stand 3 m away from the origin, and walk 1.5 m toward the origin for 3 seconds.

 B. Stand 1.5 m away from the origin, and stay for 1 second.

 C. Walk 1 m toward the origin for 1 second.
 D. Stand 0.5 m away from the origin, and stay for 2 seconds.
 E. Walk 2 m away from the origin for 3 seconds.

A. Stand about 0.8m away from the origin, and walk 1 m away from the origin for 3.5 seconds.
B. Stand 1.8 m away from the origin, and stay for 3 seconds.
C. Walk 1.3 m away from the origin for 3 seconds.

 

V-t Graphs

In a v-t graph, a straight horizontal line represents walking at a constant speed, therefore the speed doesn't change. If the line slopes upward or downward depending on the direction, the speed has changed. When the line is at 0, there is no movement.

A. Speed up for 4 seconds.

B. Walk at a velocity of 0.5 m/s away from the origin for 2 seconds.

C. Walk at a velocity of 0.4 m/s toward the origin for 3 seconds.

D. Stay for 1 second.

A. Stay for 2 seconds.

B. Walk at a velocity of 0.5 m/s away from the origin for 3 seconds.

C. Stay for 2 seconds.

D. Walk at a velocity of 0.5 m/s toward the origin for 3 seconds.

A. Walk at a velocity of 0.35 m/s away from the origin for 3 seconds.

B. Speed up, still away from the origin, for 0.25 second.
C. Slow down, now toward the origin, for 0.25 second.

D. Walk at a velocity of 0.35 m/s toward the origin for 3 seconds.

E. Slow down, toward the origin, for 0.25 second.
F. Stay for 3 seconds.

Building a Motor

Our physics class had the wonderful opportunity this thursday to build electric motors.
I love building things do this was going to be real fun ... except for the fact that it was way harder than I imagined.

The materials we needed for this project was one piece of wood, four nails, pop can to use as brushes, a stick for the axel of the motor, cork, wire, and paper clips to support the axel. And of course a power supply and magnets are needed for the motor to work.

Starting off, my partner and I had a limited time to hammer in the nails to the wood. At first, it seemd like an easy task but soon we found out the nails had to be hammered in correctly to stand up straight as well as the length between each nail was important. Soon afterwards, we began vigrously sanding the pop can and screwing the stick into the cork. Next, the paper clips were bent in a shape that would support the axel. Our motor was very near to completion with just the coiling of the wires left to do. The direction of the wire coiling was significant in the way it should be in one direction and parallel to the commutator pins.

Excited with our finished product we rushed over to test it out but were soon dissapointed with the fact that it did not work. The motor was not spinning around, or causing any spark. It stayed the same as if no current was passing through it.

With some minor changes such as baring the wires at the end, or making sure that the commutator pins touch the brushes, and even recoiling the wire on the cork about 4969693451 times ................. our motor still didn't work.

It's okay though, just getting the experience of building the motor made the motor principle and other concepts of this project more clearer. :)

Our beautiful motor :)