KInematics
Kinematics is a sub-field of physics or mechanics, that describes the motion of objects, and groups of objects without considering the forces that cause them to move. In this unit, we covered basic terms such as position, distance, and displacement, the interpretation of velocity time graphs and position time graphs and more.
Terminology
Position - The specific point in space that an object occupies relative the the origin (0,0).
Distance - The total ground that the object has covered during its motion, disregarding the direction that the object was travelling in.
Displacement - The change in position of an overall object, taking into regard the direction (negative sign means travelling backwards, while positive means travelling forwards).
Interpreting Position Time Graphs
Below is an example of a position time graph:
What it basically does is it relates the change in position to the time taken in one graph, as can be seen by the value on the x-axis (time, s), and the value on the y-axis (position, m). As the graph moves up with a positive slope, you would be going forwards relative to initial-position. As the graph flat-lines, you would be stationary and staying in the same position. As the graph decreases with a negative slope, you would be going backwards relative to initial-position.
As the slope relates position to time, it can be interpreted that the slope of the graph in individual sections would be your velocity, i.e, how fast you are moving and in which direction. A positive sign would mean that you are moving at a constant velocity forward, while a negative sign would mean you are moving at a constant velocity backward.
moving forwards
Stationary
moving backwards
Interpreting Position Time Graphs
Below is an example of a velocity time graph:
A velocity time graph relates the speed and direction in which an object is travelling as a function of time. This can yield both positive and negative values for velocity. As shown above, the y-axis of this graph shows the velocity of the object (meters per second), and the x-axis shows the time elapsed (seconds). Unlike the position time graph, the slope of the velocity time graph does not represent speed but acceleration. This can be interpreted as a constant increase of acceleration, where the object is gaining speed, positive means getting faster, while negative means getting slower. The flat-line of the graph is also interpreted as constant acceleration, where the object is maintaining the same speed.
The acceleration of the velocity time graph, as mentioned above, would be the slope of the velocity time graph at any given point. The starting velocity can be found by looking at the initial value of y as the graph starts, this is because the y-axis already expresses velocity and at x=0, aka 0 seconds in, looking at the y value would mean finding the initial velocity.
The final position, distance, and displacement are also available in the velocity time graph. We can find the distance travelled by the object by taking the area under the curve of the velocity time graph, while displacement would be the net area underneath the graph. The final position of the object can be calculated by taking the displacement as calculated and applying that to the initial position.
Connecting Position Time Graphs, Velocity Time Graphs and Strobe Diagrams
Velocity time graphs are the derivation of position time graphs. Their correlation is direct, if the position time graph is linear, the velocity time graph is fat, as the object keeps a constant velocity. If the position time graph is quadratic, the velocity time graph is linear, as the acceleration is constant.
In strobe diagrams, the velocity is constant if the length of the arrows are the same. If the length of he arrows are different, either getting larger or getting smaller, the strobe diagram represents data that either show the object accelerating or decelerating. Examples of each case are shown below:
Constant Speed
Accekerating
Decelerating
Solving problems
Usually, to solve a problem, you have to find the 6 variables of data that dictate the object's motion, they are listed below.
Xinitial
Xfinal
Vinitial
Vfinal
Acceleration
Time
Once you have these varables, you can plug them into the Kinematic equations to solve for your problem. The equations are shown below.
Projectile Motion
A projectile is a moving object in the air that ignores the air and does not interact with it. The time the projectile spends in the air is dictated by the initial horizontal velocity of the object as well as the angle of release. Below is an accurate representation of what the graphs of projectile motion would look like for 2 cases (y and x), the graphical interpretations offered take the form of a position time graph, a velocity time graph, and a acceleration time graph.
Note:
Case 1: x- horizontal motion, acceleration is always 0, velocity is constant
Case 2: y- vertical motion, acceleration is -g ( - 9.8 m/s^2), acceleration is constant
