Any measurement with the added information of direction is called a vector measurement. This added bit of information (the direction) can be very important. Whether something is on your right or on your left, above you or below you, makes a difference when you are analyzing its motion, especially if you are looking at the motions of more than one object.
A measurement without direction is called scalar and it still has units, just like any measurement, but it only indicates the scale or size of the measurement, not the direction. A measurement might be scalar because the direction is not included (like for distance or speed) or because the measurement inherently cannot have a direction (energy, mass, work).
When scalar measurements are added together, they always produce a larger result and never "cancel out". As an object travels, its distance constantly increases. Vector measurements can add together to a smaller result if they are in opposing directions. If an object travels around the Earth back to its starting point, its displacement is zero.

When you describe how far away something is, that is a measurement of distance. It could be "5 blocks", "4 train stops", "20 car lengths", "10 walking minutes", "3 light years". In SI, distance is measured in meters (which is currently based on the light year). If something is a certain distance from a point of reference, we can use distance to indicate where it is. "20 miles from downtown", "an hour's drive from my house", "two feet behind home plate" all use distance to indicate position. If a distance is given that is measured from one position to another position in a certain direction, we call this measurement displacement.
We can measure how fast something moves from one position to another if we know the time it takes to move a certain distance. If something moves a farther distance in a certain amount of time, it's moving faster. If something takes less time to go a certain distance, it's also moving faster. To put this into a mathematical relationship, we say that speed is the ratio or fraction of distance per time. So, if something travels 4 blocks in 2 minutes, it's moving at a speed of 2 blocks per minute. In SI, we measure time in seconds and speed in meters per second. A bike moving 10 meters in two seconds moves at a speed of 5 meters per second. If we include direction information, the vector measurement is called velocity.
If an object's speed or velocity changes in a measured amount of time, we can calculate how fast it speeds up or slows down or changes direction. We will again use a ratio or fraction to divide by time. The change in speed or velocity divided by time is called acceleration. Technically, a change in velocity should always be used, but speed can work for something that doesn't change direction. Since it is based on velocity which has direction, acceleration also has a direction and is a vector measurement. If the motion remains linear (just forwards and backwards, not sideways) then the change in velocity is the final velocity minus the initial velocity. If the motion is more than 1D, then using trigonometry to look at components might be needed. In circular motion, the acceleration and velocity vectors are perpendicular.
When we look at the direction of acceleration. it is the direction of velocity change. So, if velocity and acceleration are in the same direction, the object is speeding up. If they are in opposing directions, the object is slowing down. Also, an object can alow down and stop (no velocity) but still have acceleration which will speed it up in the opposite direction. If an object has no acceleration, then the velocity is not changing and it is constant.
With constant acceleration, we can use algebra to connect acceleration, velocity, distance and time. These connections are usually summarized with three equations:
Δv = a · t
Δd = (v_initial · t) + (½ a · (t)²)
(v_final)² - (v_initial)² = 2 · a · Δd
These relationships become simpler if an object starts or ends at rest, or it does not accelerate.

A graph shows a relationship between two (or more) measurements. For motion, the most useful graphs show how a measurement changes over time. A position vs. time graph shows how where an object is changes over time. It usually looks similar to an actual drawing of the object's motion. The slope of this graph shows velocity (how fast it's going). A speed vs time graph shows how an object's speed changes. If it speeds up, the graph goes up, if it slows down, the graph goes down. A velocity vs. time graph shows how velocity changes. Because it also includes direction, the interpretation is a bit more complex. If the velocity goes up in a forward (positive) direction, the graph moves up away from zero. If the velocity goes down in a backward (negative) direction, then it also moves up but starts below the x-axis and moves up towards zero. If the velocity goes down in a forward direction, the graph moves down to x-axis. If it increases in a backward direction, it also moves down but away from the x-axis. The following tables can help with the possible interpretations:

speeding up slowing down constant speed fowards or positive motion pos v pos a pos v neg a pos v zero a backwards or negative motion neg v neg a neg v pos a neg v zero a

pos a neg a zero a pos v graph moves up above x-axis graph moves down above x-axis graph is horizontal above x-axis neg v graph moves up below x-axis graph moves down below x-axis graph is horizontal below x-axis

An acceleration vs time graph for constant acceleration is always a flat line. If it is zero, then the speed and velocity vs time graphs are horizontal lines and the position and distance vs time graphs are straight lines. If the acceleration is not zero, then the speed and velocity vs time graphs are sloped lines and the position and distance vs time graphs are parabolic curves.

Newton's laws apply to objects with mass. Objects with mass have the property of inertia. Inertia is the laziness or stubbornness than mass seems to show because when mass is in the absence of any overall force pushing or pulling it, it continues to move (or not move) forever. This is Newton's first law because it is the most basic and applies to all mass all the time.
Newton's second law applies when a net force acts on an object. Any force will push or pull on an object and have an effect on its velocity. The size of the effect (acceleration) depends on the sizes of the force and the mass of the object. A bigger force on a smaller mass has more acceleration than a smaller force on a bigger mass. So, the second law is often summarized with the mathematical relationship: a = F / m   or   F = m · a. We constantly use this relationship whenever we move anything to adjust how much we pull or push on something depending on how "heavy" we think it is and how much we want to change its motion. If we find that a door is less massive than we thought and it slams open or a shopping bag is more massive than we thought and it doesn't rise off the floor like we wanted, then we again use Newton's second law to adjust our force the next time.
Newton's third law is often misunderstood because it is often ignored. The basics of the first two laws are nearly hard-wired into our brains as common sense, but when we push or pull on something we tend to ignore that we ourselves are being pushed or pulled the same amount. When we plant our feet or lean our body to move something, we use friction and trigonometry to cheat our way out of the simple meaning of Newton's third law. We use our sense of balance very automatically; it would be possibly overwhelming to have to think about all the shifts and stance adjustments needed just to stand up.
Clear, simple examples of the third law take place on an ice rink or on a skateboard or in space where friction doesn't interfere. Any force of one object on another also acts on that first object. The two forces are really just two sides or two perspectives of the same force and neither object can get more or less force than the other. The "pair" of forces are always equal in magnitude and exactly opposite in direction.

A free-body diagram shows the forces acting on an object with as few distracting details as possible. Vector arrows are drawn to indicate the size and direction of the forces acting on the object. Common forces included in a typical free-body diagram are: weight (always downward), normal or support force (usually upward from a floor or table, but can be downward from a ceiling or sideways from a wall or ramp), applied force (usually in direction of motion) and friction (usually opposing the motion).
The net force is the vector sum of the forces in the diagram. This means that when we add them together, forces in opposite directions can "cancel out".

According to Newton's second law, if an object at rest is pushed, it is accelerated and put into motion. That doesn't always happen in the real world because of friction (or good, solid construction). Moving a sofa requires a certain amount of push or pull to overcome frictional forces with the floor and get it going. Curiously, it takes less force to keep an object moving than it does to get it going. This is because friction comes in different flavors that have different strengths. Static friction acts on objects that are not moving. Kinetic friction acts on objects that are moving. Kinetic friction can also so by other names, such as rolling or sliding friction. The amount of friction that acts in a certain situation depends on the surfaces that are in contact and the amount of force that presses them together. Oil around a motor or water on a slide can help decrease friction. Cleats or spikes on shoes or deploying a parachute can help increase friction.

All masses in the universe are attracted to each other by the fundamental force of gravity. While we're still not sure how gravity works, we do know it's there. It keeps us on Earth; it keeps satellites in orbit; it keeps the Earth around the Sun. The force that attracts two objects can be calculated using Newton's law of universal gravitation.
F_grav = G · m₁ · m₂ · 1/d²   G = 6.67 x 10^-11
If the objects are more massive, the force will be greater. Our weight is noticable because the entire Earth is pulling on us. If the objects are small, the gravity is relatively insignificant. Also if the objects are farther apart, the force is less. In fact, if the objects are moved twice (2 times) as far apart, the force will be reduced to a quarter (1/2 squared) of the original amount. Likewise, if objects are brought together at half (1/2) the original distance, the force will be four (2 squared) times as much. The value of G is a constant that is the universe's conversion factor between the masses and distance of the two objects and the amount of gravitational force between them. Remember Newton's third law, that any force acts on both objects the same amount, but if one object is vastly bigger than the other, we often ignore the effect of gravity on the larger object (like a planet) and focus on its effect on the smaller object (like a satellite).

If an object accelerates in the same direction as its motion, it will speed up. If the acceleration is in the opposite direction as its motion, it will slow down. If the acceleration is at a different angle, it will change the direction of the motion (in addition to maybe also speeding it up or slowing it down). When an object moves in a perfect circle, it is accelerating exactly towards the center of the circle as it moves along the edge of the circle. The force that causes an acceleration towards the center of a circular turn is called the centripetal force. For an object in orbit, gravity supplies this centripetal force.
When we move in a circle it can feel like we are pulled or pushed to the outside the circular turn. This is actually an effect of the inertia of our mass that wants to travel in a straight line, not a curved path. Remember Newton's third law again, that if we are being pulled or pushed into a turn, we are also pulling or pushing back. We call that feeling of being pulled away from the center of circle the centifugal force, but it is as much a force as a koala bear is a bear (which is to say, that it is not a real force). The real force on us (the centripetal force) is pushing us towards the center of the circle.