Answer:
- 42 m/s
- 588 m in 14 s
- 714 m after 33 s
Step-by-step explanation:
You want to know Superman's speed, distance in 14 seconds, and distance from Lois after 33 s, if he is 1638 m from Lois after 11 s, and 1302 m from Lois after 19 s.
(a) Range of change
The rate of change of distance from Lois can be found using the formula ...
m = (y2 -y1)/(x2 -x1)
where (x, y) is (time, distance).
For the given data points, the rate of change is ...
m = (1302 -1638)/(19 -11) = -336/8 = -42 . . . . . meters/second
Superman's average rate of speed is 42 meters per second.
(b) 14 seconds
His distance in 14 seconds is 14 times his distance in 1 second:
(14 s)(42 m/s) = 588 m
Superman flies 588 meters every 14 seconds.
(c) 33 seconds
We can use the point-slope form of the equation for a linear relationship to find Superman's distance in 33 seconds.
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -1302 = -42(x -19) . . . . . . using (x, y) = (19, 1302) with m = -42
y = -42(33 -19) +1302 . . . . . add 1302, use x = 33
y = -588 +1302 = 714
Superman is 714 meters from Lois after 33 seconds.
