Q: Which of the following is the correct expression for the cosine of an angle $$\theta in a $$right triangle?

$$\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$$

Question 1

Which of the following best describes the process of adding two vectors, $$\vec{A}$$ and $$\vec{B}$$, graphically?

Accepted Answer

Place the tail of $$\vec{B} at $$the tip of $$\vec{A}$$, then draw a vector from the tail of $$\vec{A} to $$the tip of $$\vec{B}.$$

Question 2

A car moves along a straight road. Its position at $$t=0 is$$ $$x_0 = 10$$\ \mathrm{m}$$ and at t=5$$\ \mathrm{s}$$ is x_f = 35$$\ \mathrm{m}$$. What is the car's displacement?

Accepted Answer

$$\Delta x = 25\ \mathrm{m}$$

Question 3

Which of the following statements about velocity is correct?

Accepted Answer

Velocity can be positive or negative, depending on direction.

Question 4

A runner travels 100 m east and then 60 m north. What is the magnitude of the runner's net displacement?

Accepted Answer

$$\sqrt{100^2$ + 60^2$} = 116\ \mathrm{m}$$

Question 5

Which of the following is NOT a vector quantity?

Accepted Answer

Speed

Question 6

A motion diagram shows the distance between successive positions increasing over time. What does this indicate about the object's motion?

Accepted Answer

The object is speeding up.

Question 7

If a vector $$\vec{A}$$ has a magnitude of 5 units and points east, and vector $$\vec{B}$$ has a magnitude of 5 units and points north, what is the magnitude of $$\vec{A} + \vec{B}$$?

Accepted Answer

$$5\sqrt{2}\ \mathrm{units}$$

Question 8

Which of the following is the correct expression for the cosine of an angle $$	heta in a $$right triangle?

Accepted Answer

$$\cos 	heta = \frac{	ext{adjacent}}{	ext{hypotenuse}}$$

Question 9

A car starts from rest and its velocity vectors in a motion diagram get longer with each time interval. What does this indicate?

Accepted Answer

The car is speeding up.

Question 10

Which of the following is the correct SI unit for velocity?

Accepted Answer

$$\mathrm{m/s}$$

Question 11

A student walks 30 m west, then 40 m south. What is the magnitude of the displacement from the starting point?

Accepted Answer

$$\sqrt{30^2$ + 40^2$} = 50\ \mathrm{m}$$

Question 12

Which of the following is an example of a scalar quantity?

Accepted Answer

Speed

Question 13

If $$\Delta x = 120\ \mathrm{m}$$ and $$\Delta t = 10\ \mathrm{s}$$, what is the average velocity?

Accepted Answer

$$12\ \mathrm{m/s}$$

Question 14

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

Accepted Answer

It represents an object as a single point mass.

Question 15

A vector has components $$A_x = 6$$ and $$A_y = 8. $$What is the magnitude of the vector?

Accepted Answer

$$10$$

Question 16

Which of the following is the correct definition of displacement?

Accepted Answer

The change in position of an object.

Question 17

A measurement is recorded as $$3.40 	imes 10^2$ m. How many significant figures does this value have?

Accepted Answer

3

Question 18

Which prefix represents $$10^{-3}$$?

Accepted Answer

Milli

Question 19

If a car travels at $$60\ \mathrm{km/h}$$, what is its speed in $$\mathrm{m/s}$$? (Use $$1\ \mathrm{km} = 1000\ \mathrm{m}$$ and $$1\ \mathrm{h} = 3600\ \mathrm{s})$$

Accepted Answer

$$16.7\ \mathrm{m/s}$$

Question 20

Which of the following is an order-of-magnitude estimate for the mass of a typical adult human?

Accepted Answer

$$100\ \mathrm{kg}$$

Chapter 1: Representing Motion – Physics with Calculus Study Notes

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