Part (i)
Compute the slope of the line through the two points (0,0) and (4,8)
m = (y2 - y1)/(x2 - x1)
m = (8-0)/(4-0)
m = 8/4
m = 2
The slope of this line is 2, so,
velocity = 2 m/s
Part (ii)
The two points we're working with are (4,8) and (6,8). The slope is...
m = (y2 - y1)/(x2 - x1)
m = (8-8)/(6-4)
m = 0/2
m = 0
Horizontal lines always have a slope of 0 to indicate no change in height.
The velocity is 0 m/s.
Part (iii)
Same idea as the previous parts. The endpoints are (6,8) and (9,14)
m = (y2 - y1)/(x2 - x1)
m = (14-8)/(9-6)
m = 6/3
m = 2
This piece also has slope 2. This piece is parallel to the first piece. Parallel lines have equal slopes but different y intercepts.
velocity = 2 m/s
Part (iv)
(a) The average velocity from 0 to 4 seconds is the exact same as the velocity we computed earlier in part (i). The answer is 2 m/s(b) We travel 8 meters in 6 seconds, so the average velocity is 8/6 = 4/3 = 1.33 m/s approximately. You can use the slope formula for the endpoints (0,0) and (6,8) to get the same result.(c) The average velocity is 14/9 = 1.56 m/s approximately because we travel 14 meters in 9 seconds. You can use the slope formula for the endpoints (0,0) and (9,14).
As you can see, with average velocity, all we care about are the starting and ending points. We aren't concerned at all with what happens in between.
Comparing the results for part (i) and part (iv)(b), we see that the velocity has gone down. This is due to the flat portion in which you aren't moving.
