The document outlines key physics concepts related to motion, including how to interpret distance-time and speed-time graphs to determine an object's status (at rest, moving with constant speed, accelerating, or decelerating). It discusses the acceleration due to gravity (g) as approximately 9.8 m/s² near Earth's surface and factors affecting it, such as altitude and depth. Additionally, it explains how to calculate speed and distance traveled using the area under a speed-time graph.

1. MOTION 1.2 GRAPHS
PHYSICS 5054

2. OBJECTIVES
1. Determine from the shape of a distance–time graph when an object is: (a) at rest (b) moving with constant speed
(c) accelerating (d) decelerating
2. Determine from the shape of a speed–time graph when an object is: a) at rest (b) moving with constant speed (c)
moving with constant acceleration (d) moving with changing acceleration
3. State that the acceleration of free fall g for an object near to the surface of the Earth is approximately constant
and is approximately 9.8m/ s2
4. Calculate speed from the gradient of a distance–time graph
5. Calculate the area under a speed–time graph to determine the distance travelled for motion with constant speed
or constant acceleration

3. DISTANCE-TIME GRAPHS
At rest
d / m 5 5 5 5 5 5 5
t / Sec 1 2 3 4 5 6 7
1 2 3 4 5 6 7
0
1
2
3
4
5
6
Distance-Time Graph
d / m

4. DISTANCE-TIME GRAPHS
Moving with constant speed d / m 5 10 15 20 25 30 35
t / Sec 1 2 3 4 5 6 7
1 2 3 4 5 6 7
0
5
10
15
20
25
30
35
40
Distance-Time Graph
d / m

5. DISTANCE-TIME GRAPHS
Accelerating d / m 3 7 18 34 48 60 80
t / Sec 1 2 3 4 5 6 7
1 2 3 4 5 6 7
0
10
20
30
40
50
60
70
80
90
Distance-Time Graph
d / m

6. DISTANCE-TIME GRAPHS
Decelerating d / m 55 48 38 28 18 12 5
t / Sec 1 2 3 4 5 6 7
1 2 3 4 5 6 7
0
10
20
30
40
50
60
Distance-Time Graph
d / m

7. SPEED–TIME GRAPHS
At rest
1 2 3 4 5 6 7
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
V (m/sec)
V (m/sec)
V (m/sec) 0 0 0 0 0 0 0
t (Sec) 1 2 3 4 5 6 7

8. SPEED–TIME GRAPHS
Moving with constant speed
V (m/sec) 20 20 20 20 20 20 20
t (Sec) 1 2 3 4 5 6 7
1 2 3 4 5 6 7
0
5
10
15
20
25
V (m/sec)
V (m/sec)

9. SPEED–TIME GRAPHS
Moving with constant acceleration
1 2 3 4 5 6 7
0
5
10
15
20
25
30
35
40
V (m/sec)
V (m/sec)
V (m/sec) 5 10 15 20 25 30 35
t (Sec) 1 2 3 4 5 6 7

10. SPEED–TIME GRAPHS
Moving with changing acceleration
V (m/sec) 5 7 18 30 35 56 70
t (Sec) 1 2 3 4 5 6 7
1 2 3 4 5 6 7
0
10
20
30
40
50
60
70
80
V (m/sec)
V (m/sec)

11. ACCELERATION OF FREE FALL FOR AN OBJECT NEARTOTHE SURFACE OFTHE EARTH
 Acceleration of free fall is the acceleration
produced when a body falls under the influence
gravitational force of the earth alone. It is
denoted by g and its value on the surface of the
earth is
 Factors that influence the value of 'g' are
following:
 Altitude: the value of 'g' decreases as one
moves away from the surface of the Earth.
 Depth Below the Earth's Surface: the value
of 'g' decreases if one moves towards the center
of the Earth.

12. THE AREA UNDER A SPEED–TIME GRAPHTO DETERMINE THE
DISTANCE TRAVELLED
v
(m/Sec)
0 10 20 20 30 40 30 20 10 0
t (Sec) 1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
35
40
45
v (m/Sec)
v (m/Sec)

13. THE AREA UNDER A SPEED–TIME GRAPHTO DETERMINE THE
DISTANCE TRAVELLED
v
(m/Sec)
0 10 20 20 30 40 30 20 10 0
t (Sec) 1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
35
40
45
v (m/Sec)
v (m/Sec)
Step 1: Separate the curves into geometrical
shapes as shown in following graph
Step 2: Find the area of each geometrical shape.
Triangle, rectangle , trapezium and triangle.
Step 3:
Triangle: A= = 20m
Rectangle: A= = 20 x 1 = 20m
Triangle Rectangle Trapezium Triangle

14. THE AREA UNDER A SPEED–TIME GRAPHTO DETERMINE THE
DISTANCE TRAVELLED
v
(m/Sec)
0 10 20 20 30 40 30 20 10 0
t (Sec) 1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
35
40
45
v (m/Sec)
v (m/Sec)
Trapezium: A= =
Triangle: A= =
Step 4: sum of all area values is the total distance
covered by the object.
D= 20m + 20m + 60m + 120m = 220m
a h b