A) The speed of the pedestrian BC is 5 km/h
The speed of the pedestrian CD is 0 km/h
The speed of the pedestrian DE is 5 km/h
B) He arrived E since the stop after 6 hours
C) The formula for section BC is d(t) = 40 - 5t
The formula for section CD is d(t) = 20
The formula for section DE is d(t) = 50 - 5t
Step-by-step explanation:
A)
In the time-distance graph the speed is the rate of change of distance
and that mean speed = Δd/Δt ⇒ (slope of the line)
In line BC:
1. Δd = 40 - 20 = 20 km
2. Δt = 4 - 0 = 4 hours
3. The speed = 20 ÷ 4 = 5 km/h
The speed of the pedestrian BC is 5 km/h
In line CD:
1. Δd = 20 - 20 = 0 km
2. Δt = 6 - 4 = 2 hours
3. The speed = 0 ÷ 2 = 0 km/h
The speed of the pedestrian CD is 0 km/h
In line DE:
1. Δd = 20 - 0 = 20 km
2. Δt = 10 - 6 = 4 hours
3. The speed = 20 ÷ 4 = 5 km/h
The speed of the pedestrian DE is 5 km/h
B)
∵ He stop at t = 4 hours
∵ He arrived at point E at t = 10 hours
∵ 10 - 4 = 6 hours
He arrived E since the stop after 6 hours
C)
The speeds are represented by lines
The form of the equation of a line is f(x) = mx + c, where m represents
the slope of the line and c is the y-intercept (y when x = 0)
1. f(x) is d(t)
2. m is the speed
3. x is t
4. You can find c by substitute d and t by any point on the line
Line BC
Line BC has negative slope because d decreases when t increases
∵ m = -5 and c = 40
∴ d(t) = 40 - 5t
The formula for section BC is d(t) = 40 - 5t
Line CD
Line CD is a horizontal line (equation any horizontal line is y = c)
∴ m = 0 and c = 20
∴ d(t) = 20
The formula for section CD is d(t) = 20
Line DE
Line DE has negative slope because d decreases when t increases
∵ m = -5
∴ d(t) = -5t + c
To find c substitute the coordinates of point D in the equation
∵ The coordinates of point D are (6 , 20)
∴ 20 = -5(6) + c
∴ 20 = -30 + c
Add 30 to both sides
∴ c = 50
∴ d(t) = 50 - 5t
The formula for section DE is d(t) = 50 - 5t
Learn more:
You can learn more about the distance, speed, and time in
brainly.com/question/5102020
#LearnwithBrainly
