User:Inconspicuum/Physics (A Level)/Kinematics
Kinematics is the study of how objects move. One needs to understand a situation in which an object changes speed, accelerating or decelerating, and travelling a certain distance. There are four equations you need to be able to use which relate these quantities.
Variables
[edit | edit source]Before we can understand the kinematic equations, we need to understand the variables involved. They are as follows:
- t is the length of the interval of time being considered, in seconds.
- v is the speed of the object at the end of the time interval, in ms-1.
- u is the speed of the object at the beginning of the time interval, in ms-1.
- a is the acceleration of the object during the time interval, in ms-2. Has to be a constant.
- s is the displacement (distance traveled) of the object during the time interval, in meters.
Equations
[edit | edit source]The four equations are as follows:
1.
2.
3.
4.
Derivations
[edit | edit source]It is also useful to know where the above equations come from. We know that acceleration is equal to change in speed per. unit time, so:
(*)
(1)
We also know that the average speed over the time interval is equal to displacement per. unit time, so:
(2)
If we substitute the value of v from equation 1 into equation 2, we get:
(3)
If we take the equation for acceleration (*), we can rearrange it to get:
If we substitute this equation for t into equation 2, we obtain:
(4)