Question

The equation y = kx represents a proportional relationship between x and y, where k is the constant of proportionality. For a moving object, the equation d = st represents a proportional relationship between distance (d) and speed (s) or between distance (d) and time (t). Explain the different ways that you can define the constant of proportionality for this equation. Then describe some other equations that represent proportional relationships in the real world and explain why they're useful. Research on the Internet, if needed.

Answer 1

d = st

if speed is constant, there is a proportional relation between distance (d) and time (t). The constant (s) can be defined as:

s = d/t

and you can compute it knowing the distance travelled in some time

if time is constant, there is a proportional relation between distance (d) and speed (s). The constant (t) can be defined as:

t = d/s

and you can compute it knowing the distance travelled at some speed.

Acceleration (a) is defined as:

a = s/t

this equation can be rewritten as:

s = at

where a is the constant of proportionality.

Another example is Hook's law, which states:

F = ke

where F is the force applied to a spring, k is the spring constant, and e is the extension of the spring.