Kinematics
Kinematics is a branch of mechanics concerned with the motion of object, without any mention of the forces acting on the object. Kinematics is useful for being able to determine the motion of a particle when it is in a scenario where the forces acting on it are no known, such as an object in falling from a building.
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First things first, in order to understand kinematics, there are a couple of terms you will need to know. Velocity is the speed at which a particle is moving. Velocity is a vector quantity, which means that is has both a magnitude and direction. Basically, the magnitude is how fast, and the direction is which way. The direction of a particle can be signified in several ways. The simplest way is the magnitude either being positive or negative. A positive velocity means that the particle is moving in the positive direction (usually forward), while a negative velocity means the particle is moving in the negative direction (usually backwards). The direction of a particle can also be signified in several other ways, such as with a direction (eg. 10m/s West), with an angle (eg. 5 m/sat an angle of 30°), or with a combination of the two (eg. 6 m/s 60° NNW). Even though all of these can be used to signify velocity, for the study of kinematics in AP Physics, you will only be using positive velocities to signify forward motion, and negative velocities to signify backwards motion. Many students use the terms velocity and speed interchangeably, however in physics, they are two completely different things. Speed is a scalar quantity, meaning it is just a magnitude, with no direction.
Velocity is a vector quantity, meaning it has both a magnitude and direction. An example of the difference between the two is that there are two cars, one driving forward at 50 km/h, and one driving in reverse at 50 km/h. Both cars have the same speed, as they are both traveling at a rate of 50 km/h, since the cars are traveling in opposite directions, they have opposite velocities. The car traveling forward has a velocity of +50 km/h, while the car traveling in reverse has a velocity o -50 km/h. |
To put it simply. velocity is a measure of how far an object will travel in a given amount of time. So, knowing this, you can calculate the velocity of an object by measuring how far it goes and how long it takes to traverse that distance. So, the equation to find velocity ends up being v=Δd/Δt, where v is the velocity of a object, Δd is the distance from where it started (in meters), known as its displacement, and Δt is the amount of time taken to traverse the distance (in seconds). note is the difference between distance and displacement. Distance is how far an object has traveled, while displacement is how far the object has traveled relative to a certain point. A perfect example is that you decide to bike over to your friends house, which is 2 kilometers from your house. When you get to your friends house, you have traveled a total distance of 2 km, and have a displacement of 2 km, as you are currently 2 km from your starting point, aka your house. One you ride back home, you have now traveled a total distance of 4 km, however, since you are back at your starting point, your total displacement is 0 km. Velocity is typically measured in meters per second (represented as m/s). Keep in mind, that this equation only works to find the average velocity of a object moving with uniform motion. Now, for some of you, you may have never seen the symbol above that resembles a triangle, this is simply an uppercase delta from the Greek alphabet, and it is used in physics to represent the change in a quantity.
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The next topic we need to cover is acceleration. Acceleration is a change in velocity over time. So, knowing this, you can derive the equation a = Δv/Δt, where a is acceleration, Δv is the change in velocity, and Δt is the amount of time. Since acceleration is a change in velocity over time, it's unit is m/s/s or m/s2. Also, since acceleration is how much the velocity of an object changes every second, a positive acceleration means that the object's velocity is becoming "increasingly positive" (Meaning that velocity is heading toward positive infinity), and a negative acceleration means that the object's velocity is becoming "increasingly negative" (meaning velocity is heading toward negative infinity). The image to the right shows how to calculate acceleration. v1
is the initial velocity, and can also be represented as vi
or v0
(pronounced as v naught). v2 is the final velocity, and can also be represented as vf. The same goes for the times in the denominator. Keep in mind that unless the object has a constant acceleration, this equation only calculates the average acceleration of an object during the specified period of time.
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1-Dimensional Kinematics
1-Dimensional Kinematics is determining how an object will move on one single axis. This can be either horizontal motion, or vertical motion. An example of horizontal motion would be a car driving down the road. An example of vertical motion would be dropping a ball off of the roof of a building. When an object is undergoing strictly vertical motion, it is said to be in free-fall due to the fact that the the Earth's gravity is the only thing affecting the motion of the object. In order to find out how an object will move using 1-dimensional kinematics, there are seven main equations used:
v = Δd / Δt a = Δv/ Δt xf = xi + vt (yf = yi + vt for free-fall) vf = vi + at Δd = vit + 1/2at2 vf2 = vi2 + 2aΔd and Δd = 1/2(vf - vi)t |
Keep in mind, that when studying motion along the horizontal axis (x-axis), acceleration is zero, and the object moves with constant velocity, unless stated otherwise, and when study motion along the vertical axis (y-axis), acceleration is 9.8 m/s^2, unless stated otherwise.
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Projectile Motion
In order to understand projectile motion, you must first understand what a projectile is. Put simply, a projectile is any object where gravity is the only thing causing a change in the motion of the object. An object being dropped from the top of a building, a ball being thrown to another person, and a cannonball being shot out of a cannon are all considered projectiles. Now, these objects actually have something called air resistance effecting their motion, but for this class, we assume that it is negligible (the object is in a vacuum).
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Now, as shown in the third scenario in the image above, it is possible for an object to be moving along both axes at the same time. In order to find the path of the object in this scenario (know as the trajectory, you need to solve for the objects motion along each axis separately. In these problems, movement in the y-direction is simply free-fall motion (recall this means that acceleration is the acceleration die to gravity, 9.8 m/s^2), and motion in the x-direction is simply constant velocity (recall this means that acceleration is 0). In most problems, you will be given enough information to solve for time for the motion in the y-axis. Since when the object hits the ground, it is going to stop moving, the time it takes for the object to undergo its movement in the y-direction is the same time it takes to complete its motion in the x-direction. Using this, you can solve for most variables you need to know).
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