Meghan sets up her model train on a circular track that is 1 metre wide and that sits in her bedroom doorway, half in her bedroom and half in the hallway. Each round trip takes 2 seconds, and the train starts as far into the bedroom as possible. How deep into her bedroom the train engine is in terms of time is modelled by which equation?

We have a circular track that is 1 meter wide, which would mean that the diameter is equal to 1 meter.

First, we want to define this problem as a one dimensional problem. The position 0 is in the doorway, the bedroom is the positive axis, and the hallway is the negative side.

P(t) = R*cos(c*t) + R*sin(c*t).

Where R is the amplitude, in the case of the circular motion, R is equal to the radius.

If the diameter is 1m, the radius is 1m/2 = 0.5m

The equation now is:

P(t) = 0.5m*cos(c*t) + 0.5m*sin(c*t).

We also know that for t = 0s, the train is as far into the bedroom as it can, the maximum position is P = 0.5m

Then  we have:

P(0s) = 0.5m*1 + 0.5*0 = 0.5m

And we also know that the period is t = 2seconds.

The period for the sine and cosine functions is 2*pi, then:

c*2s = 2*pi

c =pi/s

The function now is:

P(t) = 0.5m*cos(t*pi/s) + 0.5m*sin(t*pi/s)

When this function is positive, this means that the train is inside her bedroom, when the function is negative, the train is outside the bedroom, when P(t) = 0, the train is in the doorway.

answer: there are 453.592 grams in a pound.

step-by-step explanation: