Question 1

Which of the following best describes a 'model' in the context of physics?

Accepted Answer

A simplified picture of reality that still captures the essence of what we want to study.

Question 2

A large number of molecules start at the origin and undergo a random walk along the x-axis. For each step, each molecule travels a distance $$d in a $$random direction. After 100 steps, what is the most likely final position of a molecule?

Accepted Answer

$$x = 0$$

Question 3

The spread of molecules due to diffusion after $$n$$ steps of a random walk is best quantified by which of the following expressions?

Accepted Answer

$$x_{\mathrm{rms}} = \sqrt{n} d$$

Question 4

If the diffusion coefficient $$D$$ for small molecules through water is known, what can you say about the diffusion coefficient for small molecules through air?

Accepted Answer

It is larger than the diffusion coefficient through water.

Question 5

The strength of the electric force $$F$$ between two ions is inversely proportional to the square of the distance $$r$$ between them: $$F \propto 1/r^2$. If the force is 1.00$$\ \mathrm{nN}$$ at a certain distance, what will the force be if the distance doubles?

Accepted Answer

$$0.25\ \mathrm{nN}$$

Question 6

A pendulum's period $$T is $$proportional to the square root of its length $$L$$: $$T \propto \sqrt{L}. If a 1-m-$$long pendulum has a period of 2 s, what is the length of a pendulum with a period of 4 s?

Accepted Answer

$$4\ \mathrm{m}$$

Question 7

Which of the following is a key difference between how physicists and biologists approach scientific problems?

Accepted Answer

Physicists tend to use more simple models and quantitative analysis.

Question 8

Which equation correctly relates the root-mean-square displacement $$x_{\mathrm{rms}} of a $$diffusing particle to the diffusion coefficient $$D$$ and time $$t in $$one dimension?

Accepted Answer

$$x_{\mathrm{rms}} = \sqrt{2Dt}$$

Question 9

In physics, why is calculus particularly important for understanding motion?

Accepted Answer

Calculus allows us to analyze rates of change, such as velocity and acceleration.

Question 10

A graph of $$\log Y$$ versus $$\log X$$ yields a straight line with slope $$r. $$What does this indicate about the relationship between $$Y$$ and $$X$$?

Accepted Answer

$$Y is $$proportional to $$X^r.$$

Question 11

A mouse has a resting heart rate of 600 beats/min, while a horse has a resting heart rate of 38 beats/min. According to the scaling law $$R \propto m$$^{-1/4}$$, what is the expected resting heart rate of an animal with a mass 16 times that of a mouse?

Accepted Answer

300 beats/min

Question 12

Which of the following is an example of a descriptive model in physics?

Accepted Answer

Newton's Law of Universal Gravitation describing the force between two masses.

Question 13

In a motion diagram, what does it indicate if the displacement vectors between frames are getting shorter?

Accepted Answer

The object is slowing down.

Question 14

Which of the following quantities is a vector?

Accepted Answer

Displacement

Question 15

A car travels 100 m east in 5 s, then 100 m west in 5 s. What is the car's displacement and average velocity over the 10 s interval?

Accepted Answer

Displacement is $$0 m$$, average velocity is $$0 m/s.$$

Question 16

Which of the following best describes the particle model in physics?

Accepted Answer

An object is represented as if all its mass were concentrated at a single point.

Question 17

If the position of an object as a function of time is given by $$x(t) = 4t^2$ + 2t$$, what is the velocity at $$t = 3 s$$?

Accepted Answer

$$v = 26\ \mathrm{m/s}$$

Question 18

Which of the following is NOT a scalar quantity?

Accepted Answer

Velocity

Question 19

A scientist is using a mathematical model to predict the trajectory of a projectile. Which of the following best describes the advantage of using such a model?

Accepted Answer

It allows for accurate predictions despite real-world complexities.

Introduction to Modelling, Quantitative Reasoning, and Motion in Physics

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