Before we discuss the dynamics of motion, there are a few terms that you must understand:

**Distance, s **(a scalar quantity)** **is the total length of space between two points.

**Displacement, s **(a vector quantity) is the distance moved in a specific direction, or an object's overall change in position.

**Speed, v **(a scalar quantity) is the distance moved per unit time.

**Velocity, v **(a vector quantity) is the rate at which an object moves in a certain direction, or the displacement per unit time.

**v= s/t**

**Acceleration, a **(a vector quantity) is rate at which velocity changes, or the change in velocity per unit time.

**a= (v-u)/t**

where v = final velocity;

u = initial velocity

t = time taken

__Motion Graphs__

We can plot a graph that describes the motion of an object:

**Displacement-Time Graphs**

These graphs have displacement on the y axis and time on the x axis. Hence, the gradient of a displacement-time graph gives the **velocity **of the object.

Graph 1:

Graph 2

Graph 3

Graph 4

**Velocity-Time Graphs**

These graphs have velocity on the y axis and time on the x axis. Hence, the gradient of a velocity-time graph gives the **acceleration **of the object.

Therefore the gradient, m:

Graph 1

Graph 2

Graph 3

Graph 4

Graph 5

Knowing all of this, you should be able to describe and object's motion based on its motion graph or vice versa:

If the graph above describes the motion of a truck, then:

**OA**- the truck is accelerating uniformly from rest for t1 seconds until it reaches a velocity of v1.

**AB**- the truck's acceleration decreases slightly in t2-t1 seconds from v1 to v2.

**BC**- the truck moves with a constant/uniform velocity of v2 for t3-t2 seconds. The truck does not accelerate.

**CD**- the truck decelerates uniformly from v2 to rest in t4-t3 seconds.

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