Question

In physics class, the students found that it takes a force of f(x) newtons to accelerate a wagon that weighs x pounds. What variable represents the input?

a) f(x)
b) x
c) force
d) wagon weight

Answer 1

The input variable in the function f(x) is (b) x, representing the wagon's weight in pounds. To find the force in newtons using a wagon's mass and acceleration, multiply the mass by the acceleration as per Newton's second law.

Step-by-step explanation:

The variable representing the input in the function f(x) newtons, where f is the function that gives the force required to accelerate a wagon weighing x pounds, is (b) x. This is the independent variable, which is the wagon's weight, and the value of x is used to calculate the corresponding force. In the context given, using Newton's second law, the force exerted on an object can be calculated by multiplying its mass (in kilograms) by its acceleration (in meters per second squared). For instance, if a wagon with mass 55 kg accelerates at a rate of 0.0255 m/s², the force on the wagon is calculated as F = ma, which equals 55 kg multiplied by 0.0255 m/s², resulting in a force in newtons.