A) The speed of pedestrian BC is 5 km/h
The speed of pedestrian CD is 0 km/h
The speed of pedestrian DE is 5 km/h
B) He reached 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 breakdown:
A)
In the time-distance graph, speed represents the change in distance with respect to time
this means speed = Δd/Δt ⇒ (slope of the line)
For 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 pedestrian BC stands at 5 km/h
For 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 pedestrian CD is 0 km/h
For line DE:
1. Δd = 20 - 0 = 20 km
2. Δt = 10 - 6 = 4 hours
3. The speed = 20 ÷ 4 = 5 km/h
The speed for pedestrian DE is 5 km/h
B)
∵ He stopped at t = 4 hours
∵ He reached point E at t = 10 hours
∵ 10 - 4 = 6 hours
He arrived at E since the stop took 6 hours
C)
<pthe line="" equations="" are="" characterized="" by:=""><pthe general="" form="" of="" a="" line="" equation="" is="" f="" mx="" c="" where="" m="" represents=""><pthe slope="" and="" c="" is="" the="" y-intercept="" value="" of="" y="" when="" x="" equals="">
1. f(x) is referenced as d(t)
2. m is the speed
3. x corresponds to t
4. You can calculate c by substituting any coordinates of a point along the line into the formula
<pline bc="">
Line BC has a negative slope because d decreases as t increases
∵ m = -5 and c = 40
Thus, d(t) = 40 - 5t
The equation for section BC is d(t) = 40 - 5t
Line CD
Line CD is a horizontal line (which follows the form of any horizontal line represented as y = c)
Thus, m = 0 and c = 20
Therefore, d(t) = 20
The equation for section CD is d(t) = 20
Line DE
Line DE features a negative slope as d decreases along with an increase in t
∵ m = -5
Thus, d(t) = -5t + c
The value of c can be determined by substituting point D's coordinates into the equation
∵ D's coordinates are (6, 20)
Thus, 20 = -5(6) + c
So, 20 = -30 + c
Adding 30 to both sides yields
∴ c = 50
Thus, d(t) = 50 - 5t
The equation for section DE is d(t) = 50 - 5t
Further Learning:
<padditional information="" regarding="" distance="" speed="" and="" time="" can="" be="" found="" in="">
</padditional></pline></pthe></pthe></pthe>
