Before all my memories of the class are entirely erased, let’s talk about some basic physics!
The first thing that you’ll usually need to know in physics is motion, so I’ll be going over that briefly here. I’m willing to talk about any physics topics that you guys want, so feel free to ask questions or bother me for a second part if you’re interested or want some help with a physics problem.
Movement along a 1-dimensional axis can be represented as follows:
In that depiction, an object moves rightwards, and it’s position is shown at 7 different points in time.
An object that is moving will have a speed and velocity. The average speed of something is calculated by dividing the distance travelled by the time it took to travel that far. For example, if something travelled 4 meters in 2 seconds, it would have a speed of 2 m/s.
Speed and velocity get slightly more complicated when trying to solve for instantaneous speed. Instantaneous speed can be thought of as the average speed of something over an infinitesimally small amount of time. For people with a passing familiarity of calculus, this will be the derivative with respect to time of the position. Unless you know calculus, you’ll probably only be given problems for which this would be incredibly easy to calculate.
Acceleration is the change in velocity over time. If a car slows to a complete halt after starting at 1 km/s over the course of 2 seconds, the magnitude of that car’s acceleration will be 0.5 km/s^2.
If something is not moving, it has no speed nor acceleration.
If something is moving at a constant velocity, it is not accelerating.
Since you really need calculus to translate position functions into velocity and acceleration functions, I’ll be overlooking those for the sake of simplicity. In basic physics, you will usually be asked about objects moving under constant acceleration.
If something is moving under a constant acceleration, its speed can be calculated using the formula v = v_i + at, where v is the final speed after the acceleration, v_i is the initial speed, a is the acceleration, and t is the amount of time that the object accelerates for.
Example
A car is stopped at an intersection. When the light turns green, the car accelerates with a magnitude of 0.25 km/s^2 for 4 seconds. What is the final speed of that car?
Using the equation provided earlier, the final speed of the car will be 1 km/s, since 0.25 km/s^2 * 4 s = 1 km/s.
Final velocity can also be calculated without knowing the amount of time if you know the distance that is travelled. The equation for this is v^2 = (v_i)^2 + 2ax, where v is the final velocity, v_i is the initial velocity, a is the constant acceleration, and x is the distance travelled.
Gravity is one of the most common forms of constant acceleration, because gravity will accelerate everything with a constant acceleration towards the center of mass. The gravity on Earth is 9.8 m/s^2, although you may have to know that more or less precisely.
Example
An object is dropped from a building on Earth that is 20 meters high. What is the final velocity of that object?
Since the object is dropped, we shall assume that it has no initial velocity. Since this is falling on Earth, we will use g (the acceleration due to gravity on Earth) as the acceleration.
v^2 = 2g(20 m) = 2 * (9.8 m/s^2) * (20 m) = 392 m^2/s^2
The final velocity will be approximately 20 m/s.
Now, these equations will not actually apply to objects on Earth that are not in a vacuum, but we make some assumptions for the sake of the math being manageable.
The final basic kinematic equation solves for position of an object under constant acceleration after a set amount of time has passed, and requires the acceleration, initial velocity, initial position, and time elapsed. The equation is x = x_i + v_i * t + 1/2 * a * t^2. If you’re familiar with calculus, you should note that this can be derived by taking the integral (twice) of a function for constant acceleration.
@HomeworkHelp ~ any questions, physics problems, or physics topics that you want to talk about?
So, thanks for the explanation!