What is velocity and displacement and the relationship between the two?

velocity is pretty much the speed in a set direction (the change in displacement not distance)
displacement is the birds eye route to the destination, opposed to the longer winding route (distance)
acceleration is the change in velocity
force can cause acceleration
increase in mass reduces acceleration

Displacement is synonymous with distance.The only difference between these two is distance is scalar that is it does not consider direction whereas displacement is a vector. Direction is a must for displacement.

If you make a right angled triangle ABC with right angle at A then to move from B to C there are two paths. One directly from B to C (hypotenuse ) and another from B to A and Then From A to C .

So displacement is the shortest distance between any two points and distance is the sum of path followed.
If you move from your place to the gas station and returned back then the net displacement is zero but the distance covered is two times the distance from your house to the gas station.

In the similar way speed and velocity are synonymous. velocity is vector so direcytion should be kept in mind
Speed does not need consideration for direction as it is a scalar.

Speed is the rate of change of distance with time
Whereas velocity is the change of displacemnt with time....../

Yes Jemma. I can appreciate your confusion here. But don't dispair just yet [ wait till you get to college for that!!!!]
Right. You know that velocity has to do with 'speed'. The important thing to remember is that velocity, displacement, force, acceleration, momentum etc belong to a group of mathematical objects called vectors
The simplest description of a vector is that it is a quantity that has two important properties. It has a size [aka a magnitude] and it has a direction associated with it.

Speed, mass, temperature, density, distance etc are quantities that have only a size associated with them. They have no direction. Because we use some sort of scale to measure them e.g a ruler, a thermometer, weighing scales etc, they are called 'scalar' quantities.

Now,

Velocity = the rate of change of DISPLACEMENT = Displacement / time

and displacement is the DISTANCE travelled IN A CERTAIN DIRECTION.

Velocity is NOT the rate of change of DISTANCE!!! Vectors cannot be the same as Scalars.

So if I said that a car is travelling with a velocity of 60 miles per hour, that would be incorrect, since I haven't said in what DIRECTION it is travelling. All I have given is its SPEED.
If I said that it is travelling at 60 miles per hour in an easterly direction, that would be a VELOCITY and not a speed. So can you see that speed is the size or magnitude of the velocity, but for a velocity to be completely described, we need its direction as well.

Let me see if I can show you the difference between displacement [ a vector] and distance [ a scaler]

Imagine you are standing on a large circle and you have to get from one side to the other which is directly opposite.
If you go around the edge, you travel around half of the circumference which is a distance of  ?r. But your displacement is calculated by how far from your starting point you are IN A STRAIGHT LINE. That is just the length of the DIAMETER of the circle. So the distance and the displacement have different values.

Acceleration = Rate of change of VELOCITY = VELOCITY / TIME

Because velocity is a vector, acceleration is a vector.

Force = mass * acceleration

Mass is a scaler but, whenever you multiply a vector by a scalar you always end up with a vector.
So, force is a vector.

Let me summarise things like this,

     Vector                        Scalar

   Weight                         Mass
   Displacement               Distance
   Velocity                       Speed

I hope I haven't added to your confusion. You can always email me if you need more help sorting these beasts out!! Good luck with your studies.