kinematics, forces and motion

We have SUVAT equations for kinematics.
$s$ is displacement, $u$ is initial velocity, $v$ is final velocity, $a$ is acceleration, $t$ is time

The table below is a really helpful things to have for your reference.

s	$s=vt-\frac{1}{2}a{t}^2$	$s=ut+\frac{1}{2}a{t}^2$	$s=\frac{t}{2}(u+v)$	$s=\frac{u^2+v^2}{2a}$
$u=v-at$	u	$u=\frac{s-a{t}^2}{2t}$	$u=\frac{2s}{t}+v$	$u=\sqrt{2as-v^2}$
$v=u+at$	$v=\frac{s+a{t}^2}{2t}$	v	$v=\frac{2s}{t}+v$	$v=\sqrt{u^2+2as}$
$a=\frac{v-u}{t}$	$a=\frac{2(vt-s)}{t^2}$	$a=\frac{2(s-ut)}{t^2}$	a	$a=\frac{v^2-u^2}{2s}$
$t=\frac{v-u}{a}$	$t=\frac{v-\sqrt{v^2-2as}}{a}$	$t=\frac{\sqrt{2as+u^2}-u}{a}$	$t=\frac{2s}{u+v}$	t

Remember the equation 1 m/s = 3.6 km/h.

a force is an influence that causes matter to accelerate

a force is represented with the letter $F$
a force is measured in newtons

Types of Forces

Forces can be categorized into several types based on their nature and the manner in which they act:

1. Gravitational Force: This is the attractive force between two masses. It is described by Newton’s Law of Universal Gravitation, which states that every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. For example, the Earth’s gravitational pull keeps us anchored to its surface and governs the orbits of planets around the sun.

2. Electromagnetic Force: This force acts between electrically charged particles. It includes both electric forces (between stationary charges) and magnetic forces (between moving charges). The electromagnetic force is responsible for the behavior of atoms and molecules, thus determining the structure of matter and influencing chemical reactions. This force can be attractive or repulsive, depending on the charges involved.

3. Strong Nuclear Force: This is the force that holds the nuclei of atoms together. It acts over very short distances, approximately the size of an atomic nucleus, and is much stronger than the electromagnetic force. The strong nuclear force binds protons and neutrons in the nucleus, overcoming the electromagnetic repulsion between positively charged protons.

4. Weak Nuclear Force: This force is responsible for certain types of radioactive decay and nuclear reactions, such as beta decay. It acts over short distances and is weaker than the strong nuclear force but stronger than gravity at the atomic level.

5. Frictional Force: This force opposes the relative motion of surfaces in contact. It can be categorized into static friction (preventing motion between stationary objects) and kinetic friction (opposing motion between moving objects). Friction is crucial in everyday life as it enables us to walk, drive, and handle objects effectively.

6. Normal Force: This is the support force exerted by a surface perpendicular to the object in contact with it. For instance, when an object rests on a table, the table exerts an upward normal force that balances the downward gravitational force on the object.

7. Tension Force: This force is transmitted through a string, rope, or cable when it is pulled tight by forces acting from opposite ends. It acts along the length of the string or rope and is directed away from the object.

8. Applied Force: This is the force exerted on an object by an external agent. For example, when you push a door open, the force you apply to the door is an applied force.

9. Spring Force: This force is exerted by a compressed or stretched spring, described by Hooke’s Law. It states that the force exerted by a spring is proportional to its displacement from the equilibrium position, given by F=−kx, where k is the spring constant and x is the displacement.

acceleration in meters per second squared is equal to force in newtons divided by mass in kilograms

$a\cdot \frac{m}{s^2}=\frac{F\cdot N}{m\cdot kg}$
$a=\frac{F}{m}$

$\frac{F}{m}\cdot \frac{m}{s^2}=\frac{F\cdot N}{m\cdot kg}$
$F\cdot s^{-2}=F\cdot N\cdot m^{-1}\cdot k{g}^{-1}$
$1=N\cdot m^{-1}\cdot k{g}^{-1}\cdot s^2$

momentum in kilograms times meters per second is equal to mass in kilograms times position , velocity , acceleration , jerk in meters per second
$p\cdot kg\cdot \frac{m}{s}=m\cdot kg\cdot v\cdot \frac{m}{s}$
$p=mv$