Q: A ball is thrown horizontally from a cliff with an initial speed of $$10\ \mathrm{m/s}. $$Ignoring air resistance, how far will it travel horizontally in 2 seconds?

$$10 \times 2 = 20\ \mathrm{m}$$

Q: A car accelerates from rest at $$2\ \mathrm{m/s^2$}$$ for 5 seconds. What is its final velocity?

$$v = 0 + 2 \times 5 = 10\ \mathrm{m/s}$$

Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$What is the formula for its maximum height?

$$H = \frac{v_0$^2 \sin^2$ \theta}{2g}$$

Q: If two forces $$\vec{F}_1$$ and $$\vec{F}_2$$ act at an angle $$\theta to $$each other, what is the magnitude of the resultant force?

$$\sqrt{F_1$^2 + F_2$^2 + 2 F_1$ F_2$ \cos \theta}$$

Question 1

A hiker walks 4 km east and then 3 km north. What is the magnitude of the resultant displacement?

Accepted Answer

$$\sqrt{4^2$ + 3^2$} = 5 km$$

Question 2

Which of the following best describes the difference between speed and velocity?

Accepted Answer

Speed is a scalar quantity; velocity is a vector quantity.

Question 3

A ball is thrown horizontally from a cliff with an initial speed of $$10\ \mathrm{m/s}. $$Ignoring air resistance, how far will it travel horizontally in 2 seconds?

Accepted Answer

$$10 	imes 2 = 20\ \mathrm{m}$$

Question 4

Which equation correctly relates acceleration ($$a$$), initial velocity ($$u$$), final velocity ($$v$$), and time ($$t) in $$uniformly accelerated motion?

Accepted Answer

$$v = u + a t$$

Question 5

A car accelerates from rest at $$2\ \mathrm{m/s^2$}$$ for 5 seconds. What is its final velocity?

Accepted Answer

$$v = 0 + 2 	imes 5 = 10\ \mathrm{m/s}$$

Question 6

Which of the following is NOT a vector quantity?

Accepted Answer

Distance

Question 7

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What is the formula for its maximum height?

Accepted Answer

$$H = \frac{v_0$^2 \sin^2$ 	heta}{2g}$$

Question 8

Which law states that an object at rest stays at rest and an object in motion stays in motion unless acted upon by a net external force?

Accepted Answer

Newton's First Law of Motion

Question 9

A block of mass $$m$$ slides down a frictionless inclined plane of angle $$	heta. $$What is the acceleration of the block?

Accepted Answer

$$a = g \sin 	heta$$

Question 10

If two forces $$\vec{F}_1$$ and $$\vec{F}_2$$ act at an angle $$	heta to $$each other, what is the magnitude of the resultant force?

Accepted Answer

$$\sqrt{F_1$^2 + F_2$^2 + 2 F_1$ F_2$ \cos 	heta}$$

Question 11

A skydiver reaches terminal velocity during free fall. Which statement is true at terminal velocity?

Accepted Answer

The force of gravity is balanced by air resistance.

Question 12

A car travels 100 m north, then 100 m east. What is the total displacement?

Accepted Answer

$$\sqrt{100^2$ + 100^2$} = 141.4 m$$

Question 13

Which of the following is the correct kinematic equation for displacement ($$s) $$under constant acceleration?

Accepted Answer

$$s = u t + \frac{1}{2} a t^2$

Question 14

A 5 kg object is pulled by a force of 20 N. What is its acceleration?

Accepted Answer

$$a = \frac{F}{m} = \frac{20}{5} = 4\ \mathrm{m/s^2$}$$

Question 15

Which statement about equilibrium is correct?

Accepted Answer

The net force acting on the object is zero.

Question 16

A ball is dropped from a height of 20 m. Ignoring air resistance, how long does it take to reach the ground? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{40}{9.8}} \approx 2.02 s$$

Question 17

Which of the following best describes inertia?

Accepted Answer

The tendency of an object to resist changes in its state of motion.

Question 18

A person pulls a box with a force of 50 N at an angle of $$30^\circ$$ above the horizontal. What is the horizontal component of the force?

Accepted Answer

$$F_x = 50 \cos 30^\circ = 43.3 N$$

Question 19

An Atwood machine consists of two masses, $$m_1 = 3$ kg and m_2$ = 5 kg$$, connected by a string over a frictionless pulley. What is the acceleration of the system? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$a = \frac{(m_2$ - m_1$)g}{m_1$ + m_2$} = \frac{(5 - 3) 	imes 9.8}{3 + 5} = 2.45\ \mathrm{m/s^2$}$$

Vectors, Kinematics, and Newton's Laws: Study Guide and Syllabus Overview

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