While studying physics, there are many topics that the students find difficult because of the formulas and numerical that it contains. One such topic, which is both typical as well as important, is the ‘Kinematics Physics Equations.’ In this blog, we attempt to explain the basics of the topic in concern, along with certain techniques to solve the associated problems. Out of the three branches of mechanics, namely kinematics, dynamics, and static, we try to elaborate on the kinematics and give you a slight detail of each of the other branches.
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A Brief Overview of Kinematics
Kinematics is the branch of mechanics that describes the motion of objects using words, diagrams, numbers, graphs, and equations. A kinematics student intends to develop the mental models that serve to describe the motion of real-world objects. The study of kinematics gives a holistic view of the entire movement of the objects, along with its direction and time duration. But, in the information named above, the only missing information is what describes motion in kinematics. Further, while describing the motion in kinematics, the four main parameters that come into play for the descending motion are displacement, velocity, acceleration, and time.
Parameters of Kinematic Physics Equations
Here are all the four main parameters of the kinematics physics equations in greater detail.
Distance and Displacement
The first parameters to understand motion in kinematics are displacement and distance. Displacement refers to the change in the position of any object from the state of rest to motion or vice versa. It serves as a parameter for helping to understand the extent of an object’s movement, depending on the direction. It, in short, helps in understanding the shortest route taken to one place to another. On the other hand, distance is a measure of the actual distance covered. Here are the main formulas that help in the calculation part:-
displacement=final position-initial position=change in position
- S=Xf-Xi=change in X
- Xf=final position
- Xi=initial position
- S=displacement
- The distance formula is as given below:
- d=sum of the actual distance
Velocity
The second in the list of parameters of kinematics is velocity. This parameter helps in describing the movement of the motion. To elaborate, velocity means how fast an object moves from a certain point to another in a given direction. In short, it helps in determining how long an object takes to move from one place to another and, in turn, in calculating the speed. The calculation of both the speed and velocity will give the average velocity.
The formula for velocity is:-
v = Δs/Δt
Acceleration
The third parameter of the kinematics physics equations is acceleration. Knowing this parameter will help in describing the speed as well. Acceleration refers to the change in velocity each moment. With it, one can easily determine how much an object accelerates from one point to another. According to the formula, there is an inverse relationship between acceleration and time. So, if time increases, then the acceleration decreases, and vice versa.
The formula for acceleration is:-
a=Δv/Δt
Time
The fourth parameter of the kinematics physics equations is time. Now, this parameter plays a chief role in kinematics physics equations. It is a single reference point for all the three parameters named above. Without calculating the time, you cannot calculate the other parameters in concern.
Kinematics Physics Equations: Explained
Now that you know all the various parameters of the kinematics physics equations, here are the various equations that form up with these parameters. Let’s understand each equation in detail.
v2=v1+aΔt
In this equation, the first task is to calculate the slope of the diagonal line. This slope is the change in velocity divided by the change in time, which in turn equals the acceleration.
a = v2–v1/t2–t1
One must rewrite t2 – t1 as Δt
a = v2−v1/Δt is equation 1.
On rearranging these equations, you can find the value of v2.
One must rearrange it to get v2 on the left side.
This gives the slope-intercept form of a line, which is:-
v2 = v1 + aΔt
Δx=(v+v0)t/2
To get the next kinematics physics formula, derive an expression for the displacement of an object, take the value of time as Δt and calculate the displacement finally:-
S = vΔt
Furthermore, the displacement of the object is equal to v1Δt, and the product v1 is equal to area A1.
So A1 = v1Δt
Then, A2 = (V2−V1Δt)/2
Now adding A1 and A2
s = A1 + A2
Substituting for A1 and A2 gives
s = (v2−v1)/2Δt + v1Δt
Now simplifying it would give
s = (v2+v1)/2Δt. This is in equation 2.
s = v1Δt+aΔtsq/2
To find the third equation, eliminate the v2. Let’s find the steps for the elimination.
v2 = v1 + aΔt
Now make use of algebra to make the left side of the formula look like the right side
v2 + v1 = v1 + aΔt+ v1
v2+ v1 = 2v1 + aΔt
Furthermore, multiply both the sides by 12Δt
s = (v2+v1)/2Δt= (2v1+aΔt)/2Δt
s = v1Δt+aΔtsq/2 (This is formula 3)
v2sq= v1sq + 2as
In formula 4, eliminate the time variable, or Δt
Now, rearrange the first equation and keep the acceleration part on the right.
a = v2−v1/Δt
Then, multiply the left side of equation 1 by the left side of equation 2 and vice-versa.
s = (v2+v1)/2Δt
as = [(v2–v1)/2Δt][v2−v1/Δt]
Then Δt cancels out and in turn simplifies the equation.
2as = v2sq−v1sq
This formula is almost always written as:
v2sq= v1sq + 2as (This is formula 4)
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