### Analyzing position-time graphs - mirnay

Objectives
You will be able to:
o Relate the slope of a position-time graph to speed
o Determine speed using position-time graphs
o Describe the type of motion indicated in a positiontime graph; motion with constant speed or accelerated
motion
1.
Recall that:
A position vector is a vector that
joins the origin to the new position
of the moving object.
2. time interval= ∆t=final timeinitial time.
displacement=
∆d=final position- initial position.
3.
4.
A position time graph can:
- describe the motion of an object
- determine the position of the object
at a certain time
- determine the time of an object for a
certain position.
Motion with a constant speed
(uniform motion)
Motion with a changing speed (
Accelerated motion)
Motion with a constant speed
- Position -time Line of best fit:
- Relationship:
-Equation : y=
Motion with a changing speed
- Position -time Line of best fit:
- Relationship:
-Equation : y=
 Uniform motion ( constant speed)
Position-time graph: straight line
 Accelerated Motion ( varied speed)
Position –time graph: parabola
Position time graph
Data
Y= mx+b
Where:
y is the position at a certain
time
X is the time
m= slope
B= y-intercept
Calculating slope
-( rf: ch: 1 section 3)
- Absolute value of slope= speed
2. y-intercept
Represents the initial vector position of the
object .
3. A line with a greater slope (steeper line )
represents a constant motion with a
higher speed.
1.
App:
Find the speed and initial vector of the
object whose motion is representing by
the graph + question II from the
worksheet
Describe the motion of an object whose
motion is described by the following
equation: y= -2 x+4
Accelerated motion of a moving
towards the origin with increasing
speed
Accelerated motion of a moving object
towards the origin with a decreasing
speed
Object moving away the
origin with an increasing
speed
Equation:
Y= ax² + bx +c
Where a= half of the acceleration
(rf . Section 2.4 How Fast?)
b= initial (starting)velocity
c= initial position
App:
Describe the motion of an object
whose position –time is
represented by the following
equation:
Y (m)= 2 x² + 3x +4
- 2 types of linear motion:
a. Uniform motion where the speed is kept constant:
•
Position- time graph is represented by a straight line
where : absolute value of the slope= speed
b. Accelerated motion where the speed is changing over
time.
• Position – time graph is represented by a parabola.
Solve : question II & III from the worksheet
 Solve questions p: 53 no.54 &55