Embedded Files
by Y11 students
This page contains Physics contents discussed in class and re-written by students in prose form to show how well they understood the materials with some elements of creativity and link to the holistic being that the school is promoting through the P.I.A.G.E.T. values. Classmates read the contributions when doing home revisions and/or serve as peer support to others may have fall short of the standard, failed to earned the content-based badges.
Contributions in this page are also part of the 5% PROJECT component of the Final Grade in each term of the school year.
Equations of Motion a.k.a. Kinematic Equations
As derived by Hindranata, 9 August 2020
YouTube video
Kinematic Equations
Motion is the state of change in position of an object over time. It is described in terms of displacement, distance, velocity, acceleration, time and speed. Running, throwing a ball straight, and even simply taking a walk are all everyday examples of motion. The relations between these quantities are known as the equations of motion.
In case of uniform acceleration, there are four equations of motion which are also known as the laws of constant acceleration. Hence, these equations are used to derive the components like displacement(s), velocity (initial and final), time(t) and acceleration(a). Therefore they can only be applied when acceleration is constant and in a straight line motion. The four equations are shown at the left.
In these equations, s is the displacement of the object, u is its initial velocity, v as its final velocity, a is the acceleration, and t is the time of motion.
NOW, where did these equations come from?
1st Equation
We know from its definition that acceleration equals change in velocity / time of motion. Therefore, acceleration can be rewritten as (final velocity - initial velocity) divided by the time of travel. Hence, a = (v - u) /t or at = v - u, which can lead us to v = u + at (1st equation).
2nd equation
We start with what we have, v = u + at or the 1st equation. Rearranging it gives us t = (v-u) / a. Also, we know that, resultant displacement = average velocity × time. When these two equations are combined, we we will have an equation for displacement, s = [(v+u)/2] × [(v-u)/a] or s = (v² – u²)/2a which can be further simplified into 2as = v² – u² or v² = u² + 2as (2nd equation).
3rd equation
We know that displacement = average velocity × time. Also that average velocity = (u + v) / 2. Therefore, displacement s = (u + v) / 2 × t. Also, from v = u + at, we have s = (u + u + at) / 2 × t = (2u + at) / 2 × t. This is simplified to get s = ut +½ at² (3rd equation).
4th equation
When the first equation is substituted into equation two, it will result in the fourth equation, v² = u² + 2as.
Reading the graph
In the first three seconds an object is at rest(represented by the black line), in the next two seconds the object moves towards the reference zero point and to the opposite direction(represented in the red line), again for the next three seconds the objects is at rest(represented by the purple line) and finally the object again moves towards the zero point and goes to the positive direction for seven seconds.
displacement-time graphs
In order to find the acceleration of the object from the velocity-time graph above, we simply find the slope of the functions. In the case of the orange line on the graph, the acceleration(slope) is (1m/s2) and for the pink line the acceleration(slope) is(0.5m/s2). It is clear that in this case the acceleration is constant from (0-5)sec and from (5-15)sec. Finding the acceleration through a velocity time graph is by finding the gradient of the sloping line.
Velocities from GSJ a-t Graph Workaround
Tips from Kiesha, 9 August 2020
Google Science Journal has been really useful to help science students carry out experiments virtually, especially during this pandemic going on. With regards to our topic, Kinematics, GSJ is really useful in helping us to find out average velocity or change in velocity. This can be done by two ways, measuring the light intensity or by acceleration. In this essay, I will be discussing the acceleration time graph and how to determine the average velocity from it.
To do this, you only require your phone. Firstly, you just need to open the Accelerometer Y sensor, then set the phone face up on a flat, smooth surface. Remember that you should keep the phone flat on the surface. Put a label on where the starting point of the phone is. Slide the phone quickly in the direction of the Y axis. When you stop the phone, wait for a second and then slide it back to where it starts. Repeat the movement for a few times and you can see a pattern in the graph like the one shown at the right.
When the graph is showing a positive spike, it shows that the phone is accelerating. When the graph is showing a negative spike, it shows that the phone is decelerating.
From the graph shown above, we can determine the change in velocity. To find it, we just need to calculate the area under the graph. The area under the graph within a time interval is the change in velocity during that time interval itself. But how do you find the area?
Let’s take the graph down below as an example.
To measure the area of the graph above you simply need to measure the area of the blue rectangle (4 x 3 = 12), the green triangle ( 4 x 4 : 2 = 8) and the red triangle (2 x 2 : 2 = 2). Then, you just need to add them. There you have it, the total velocity of the item.
a-t graph in GSJ
Simpler a-t graph
Everything You Need to Know About Freefall
Collated by Justin, 9 August 2020
I’m sure that at one point in our lives, we have all tried jumping. We all have felt being in the air before dropping right down back onto our two feet. In the few moments that we are falling to the ground, we are in what’s called a freefall motion.
In Physics, a freefall motion occurs when gravity is the only force that is acting on the object. Interestingly, the motion of an object thrown upwards can also be called a freefall as long as only gravity acts on it.
It is good to take note that not all falling objects are considered to be in freefall. There are some characteristics that all freely falling objects share.
Freely falling objects do not encounter air resistance or any other force that could cancel the effect of gravity.
All freely falling objects change speed at the a certain constant rate called acceleration due to gravity amounting to - 9.81 m/s².
Solving Physics problems on freefall is not different from solving problems about objects moving at uniform acceleration. We can use the four kinematic equations that we have learned earlier in the year, replacing all the a's by - 9.81 m/s². This is as you can determine the initial and final velocity of the object rather easily, you can then also determine the amount of time assuming that this is set within an experiment and not a word problem; it is also possible to determine the displacement. This allows us to get any of the quantities needed to use the four kinematic equations.
At home, if you wish to try out the freefall concept for yourself, here is an experiment that you can do.
You need your devices like handphone or tablet with a camera to record a video.
You also need a straight wall with marks of heights. You can paste measuring tapes along the vertical.
To gather data to determine the acceleration of freefall, drop a dense object from a height while recording a video of its fall.
Make a table of values. Displacement of dropped object can be measured by looking at the video and the time as indicated in the video as well. Velocity at any time of its fall can then be calculated.
Graph the velocity values against time and draw a best-fit line. Find the gradient of this line, or the acceleration of the freefall.
Compare the gradient calculated to the magnitude of the accepted value of acceleration due to gravity [acceleration of freefall] and reflect on the possible sources of error.
The PhET Projectile Motion Simulation
Reviewed by Derrel, ? September 2020
Newton's Laws of Motion
Notes from Nico, ? August 2020
Report abuse