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            <h1>Kinematics</h1>
            <span class="subheading">Unit 1</span>
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        <p><b>Kinematics</b> is known as the study of how things move and is the first branch of Mechanics. The foundation of Kinematics was laid out by famous astronoumer <b>Galileo Galilei</b>. His work was widely spread throughout Europe and his book "Two New Sciences" opened the way to treating physics mathematically. For instance, he derived the <b>Kinematic Equations</b>.

          <img class="img-fluid" src="https://images.unsplash.com/photo-1593240637899-5fc06c754c2b?ixlib=rb-1.2.1&ixid=eyJhcHBfaWQiOjEyMDd9&auto=format&fit=crop&w=1880&q=80" alt="Galileo Galilei">

        <span class="caption text-muted">Galileo Galilei</span>
        <h1 id="in">Key Terms</h1>
        <p>
          <ul>
            <li>Reference Point & Reference Frame: observations from different point of views or references. A reference point is a comparison between objects in motion. A Reference Frame is a reference point with a set of directions. </li>
              When you are sitting in a car and pass another car, you feel like you are stationary and you use other objects as references: neighbouring cars as a reference point to determine that your car is moving and someone standing outside could see that the cars are moving <b>relative</b> to him/her.
              <img class="img-fluid" src="img/post-sample-image - 副本.jpg" alt="Relative Motion Example">
              <span class="caption text-muted">Relative Motion Example</span>
            <li>Relative: Formulated by Albert Einstein, relative is the relation between multiple points and that all motion must be defined relative to a reference frame.</li>
              For instance, you are currently moving relative to the Earth who is rotating constantly, but you aren't moving relative to your room that you are inside of.
            <li>Scalar: a quantity having only magnitude</li>
            e.g. 5m
            <li>Vector: a quantity having both magntide and direction. Vectors are denoted with an arrow above the variable and are graphed with an arrow as well.</li>
            e.g. 5m[West]
            <li>Position: place where an object is located or has been put. In physics, this is usually represented numerically as a vector.</li>
            <li>Distance: the total quantifiable amount an object travelled. This is a scalar value because there is no direction. The distance ignores the direction travelled and only accounts for the total amount travelled in that specific period. </li>
            <li>Displacement: the change in position(final position - initial position). This is a vector quantity.</li>
            <li>Speed: rate at which an object is able to move. Speed depends on distance.</li>
            <li>Velocity: speed of an object in a given direction. Velocity depends on displacement</li>
            <li>Instantaneous: a quantity at a particular moment in time.</li>
            <li>Tangent Line: a linear line that touches the graph at one particular point.</li>
            <li>Acceleration: the change in velocity over a certain amount of time. Every second, the velocity increases/decreases by a certain magntiude.</li>
            e.g. Cars stepping on the gas pedal.
            <li>Uniform & Non-Uniform: Uniform is motion at a constant speed in a straight line whereas Non-uniform is motion with a change in either speed or direction.</li>
            <li>Vector Diagram: a diagram used to show the motion travelled</li>
            <img class="img-fluid" src="img/post-sample-image - 副本 (6).jpg">
            <span class="caption text-muted">Vector Diagram Example</span>
          </ul>
        </p><br>
            <h1>Graphs</h1>
            <h2>Introduction</h2>
        <p>
            In Physics, it is crucial to show rather than to tell considering the complexity of some of its concepts. Which is why graphing the situation is a great solution.
            The concepts of distance, displacement(position), speed, velocity, and acceleration can be graphed over a time x-axis.
            <br>Let's say Jade walks 4 metres east in 3 seconds then walks 3 metres to the west in 2 seconds at a constant velocity.<br>
            So the distance is: 4 metres + 3 metres = 7 metres <br>
            If Jade walked 4 metres east but then 3 metres west, she really only walked 1 metre east of her initial position; this is her displacement.<br>
            If Jade travelled for 5 seconds in total, then her speed would be 7m/5s = 1.4m/s
            <img class="img-fluid" src="img/post-sample-image - 副本 (2).jpg">
            <span class="caption text-muted">Distance, Displacement/Position, and Speed Graphs</span>
            <br>If Jade had a displacement of 1m[East], then her velocity would be 1m[East]/5s = 0.2m/s[East].<br>
            <img class="img-fluid" src="img/post-sample-image - 副本 (3).jpg">
            <span class="caption text-muted">Velocity & Acceleration Graph</span>
            <br>As shown in the graph, the acceleration is zero. Since Jade had travelled at a constant velocity, she wouldn't have any acceleration. If she did, then there would be a horizontal line at the magnitude of the acceleration.<br>
            If Jade was travelling in the same direction for the whole period, you can imagine that the magnitude of the distance and displacement travelled would be equal, thus speed and velocity as well. If an object changes direction, then the average speed and average velocity wouldn't be equal because the distance and displacement wouldn't be on which they depend on respectively. <br>
            Let's say Jade then walks 2m south for 2 seconds, which is 2D Motion. The distance and speed graphs will change but overall look relatively the same, but the displacement and velocity graphs will be different with the addition of a second graph to show the vertical motion.<br>
            To calculate the magnitude of displacement, you would need to use the Pythagorean Theorem if the triangle created is a right-triangle and the cosine law(which requires an angle that can be estimated) if it isn't. To calculate the direction, you would need to use the trigonometric ratios if it was a right-triangle and the sine law if it isn't.<br>
            <img class="img-fluid" src="img/post-sample-image - 副本 (5).jpg">
            <span class="caption text-muted">2D Displacement & Velocity Calculations</span>
            With it, you could then graph it.<br>
            <img class="img-fluid" src="img/post-sample-image - 副本 (4).jpg">
            <span class="caption text-muted">2D Displacement & Velocity Graphs</span>

        </p>
        <h2>Analysis</h2>
        <p>
          To go from a position-time graph to a velocity-time graph, we need to find the slope of the line. If the line is horizontal, that would mean that the object didn't move and therefore have a velocity of zero(horizontal line at zero). If the line is slanted, then the object did move and therefore there is velocity(horizontal line at the slope value on the v-t graph). If the line isn't linear, then we can use tangent lines to find the instantaneous velocity at particular moments in time to then be able to draw a line on the velocity-time graph(slanted line). This slope-like formula can also be seen on the average velocity formula itself: the displacement/position(y-value) over the time interval(x-value) equals the average velocity.
          <br>To go back from a velocity-time graph to a position-time graph, you would need to find the area that is under the line. This can be seen in the average velocity formula by isolating for displacement to get d=V*t which resembles the area of a rectangle formula. If the line is slanted, you would have to treat the area as a triangle and divide V*t by 2.
          <br>To go from a velocity-time graph to an acceleration-time graph, we would need to find the slope of the line on the velocity-time graph. If the line is completely horizontal, then that would mean the velocity is constant therefore the acceleration would be zero(horizontal line at zero on a-t graph). If the line is slanted, then the velocity would be changing over time therefore there would be acceleration(horizontal line at the acceleration value on the a-t graph). This slope-like formula can also be seen on the average acceleration formula itself: the velocity(y-value) over the time interval(x-value) equals the average acceleration.
          <br>Going from an acceleration-time graph to a velocity-time graph is the same process as from the velocity-time graph to position-time graph. It can be seen in the average acceleration formula after isolating for velocity to get V=A*t.
            A positive or negative slope would mean the direction of the vector. A positive line would mean one way and a negative line would mean the opposite way.
            <img class="img-fluid" src="img/post-sample-image - 副本 (7).jpg">
            <span class="caption text-muted">Transitioning Between Graphs</span>
        <h1>Kinematic Formulas</h1>
        </p>
          Initial and Final Velocity are basically the instantaneous velocity at the very start of a time interval and at the end respectively. They are used in the Kinematic Formulas.
          The Kinematic Formulas are the main takeaway from the Kinematics Unit. They are formulas that were derived from previous mentioned formulas. Each formula is missing a certain Kinematic Variable.
          <br> <img class="img-fluid" src="img/post-sample-image - 副本 (8).jpg">
          <span class="caption text-muted">The Big 5</span>

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