So let's talk about equations of motion. So the first thing you need to identify when dealing with problems associated with equations of motion is if the object that's moving, if it's moving at constant speed or with constant acceleration. So let's start with constant speed.
If an object is moving with constant speed, this equation becomes important. d is equal to vt. Now, d can be used as distance or displacement. So you can think of distance as equal to rate multiplied by the time, or distance as equal to speed multiplied by the time, same thing.
Or you can think of displacement as equal to velocity multiplied by time. And of course, you can rearrange this equation. If you're calculating the speed, which is the same as v, speed is equal to distance. Divided by time Velocity on the other hand velocity is equal to the displacement over time Now remember, velocity is a vector. Speed is not.
Velocity has both magnitude and direction. Speed only has magnitude. Speed is always positive.
However, velocity can be positive or negative. So speed is the absolute value of velocity. Now if you're wondering what the difference between distance and displacement is, distance is a scalar quantity like speed. Displacement is a vector quantity like velocity. So let's say if a person travels 8 meters east and 3 meters west.
The total distance that this person travels is 11 meters. Distance is always positive. Now, the displacement, however, is different. During the first part of the trip, the displacement is positive because he's traveling east towards the positive x-axis. But during the second part, he's traveling west, and that's negative.
So to calculate the displacement, you would add these two, positive 8 plus... negative 3 so it's positive 5 meters if you look at the difference between the initial initial position and the final position you would also get 5 so that's displacement displacement is the change in position So you can calculate that along the x-axis, the final position minus the initial position, so that's horizontal displacement. Or you can calculate the vertical displacement, dy, which is also the final position minus the initial position.
Now, going back to velocity. If you want to calculate the velocity in the x direction, you need to take the horizontal displacement, which is the final position minus the initial position, and then divide it by the time. If you want to calculate the vertical velocity, in the y direction, you need to take the final position minus the initial position in the y direction divided by t.
So pay attention to the direction in which you're calculating velocity. Is it in the x direction or in the y direction? Now let's move on to the formulas you need to know when dealing with constant acceleration. Keep in mind, velocity is the rate at which displacement is changing. Acceleration is the rate at which a velocity is changing.
So as we saw, velocity was displacement over time. Acceleration is the change in velocity over time. So acceleration is delta V over delta T. Particularly, this is average acceleration, so it's V final minus V initial divided by T.
Now, if you were to rearrange this equation, if you multiplied A by T and then added V initial, you would get V final. You would get V final. is equal to v initial plus 18. By the way, for those of you who want example problems on how to use these formulas, check out the links in the description section below.
I'm going to post some videos like on kinematics, projectile motion, free fall problems, and in order to solve these problems, you need to use these formulas. So it'll give you the practice that you need. The next formula you want to be familiar with is this one.
V final squared is equal to V initial squared plus 2AD. Also pay attention to units velocity is typically in units of meters per second feet per second miles per hour so forth Acceleration is like meters per second squared Feet per second squared and things like that it could be kilometers per square hour It's unit left over time squared Now, recall that for constant velocity, we had this equation, d is equal to vt. For constant acceleration, it's very similar, but because we have acceleration, the velocity is changing. So you need to use the average velocity.
Whenever you want to find the average of two numbers, you need to add up the two numbers and divide by two. So dividing by 2 is the same as multiplying by 1 half, and then we're going to add the initial and final velocity values in this time interval. So that's the next equation you need to calculate displacement.
It's the initial velocity plus the final velocity divided by 2 multiplied by t. But it comes from this equation, it's just that we're using average velocity instead. Now, displacement is also equal to v initial t plus 1 half a t squared. Now, I've seen different variations of this formula, because, mind you, you can replace displacement with final position minus initial position in the x or y direction. If you replace it with the x direction and solve for final position, you get this equation.
Final position is equal to initial position plus the v initial t plus 1 half a t squared. In this case, the initial velocity and the acceleration are all in the x direction. Now, you can apply the same formula in the y direction, and it's going to look like this.
This case, the initial is in the y direction and the acceleration is in the y direction. This is important for free fall problems and projectile motion problems. So those are the main kinematic formulas that you need to be familiar with when dealing with motion. Now for those of you who might be taking calculus, here's some other things you want to know. S represents position.
The derivative of the position function will give you the velocity function. And the derivative of the velocity function will give you acceleration. Now if you want to get the velocity function from acceleration, it's equal to the antiderivative of the acceleration formula plus the constant of integration, the constant c.
And if you want to get the position function, it is the integral of the velocity function and then plus the constant c. So that's basically it for this video. So for those of you who want example problems on how to use these equations, feel free to check out the links in the description section below.