Q: Usain Bolt ran 100 meters in 9.58 seconds. What was his average speed in miles per hour?

$$\displaystyle 10.44\ \mathrm{m/s} \times \frac{1\ \mathrm{mi}}{1609\ \mathrm{m}} \times \frac{3600\ \mathrm{s}}{1\ \mathrm{h}} \approx 23.4\ \mathrm{mi/h}$$

Q: If 8 billion people stood on the equator, each separated by 2 meters, how many times would the line of people circle the Earth? (Earth's equator $$= 40,000\ \mathrm{km})$$

$$\displaystyle \frac{16 \times 10^9$\ \mathrm{m}}{4 \times 10^7$\ \mathrm{m}} = 400$$

Q: During a 90-degree swing, a pendulum of length $$2\ \mathrm{m}$$ travels a distance equal to a quarter of the circumference of a circle. What is this distance?

$$\displaystyle \frac{1}{4} \times 2\pi \times 2\ \mathrm{m} = \pi\ \mathrm{m}$$

Question 1

A car travels 150 miles from New York to Albany. It covers the first half of the distance at 45 mi/h and the second half at 75 mi/h. What is the car's average speed for the entire trip?

Accepted Answer

$$\displaystyle \frac{150\ \mathrm{mi}}{2.7\ \mathrm{h}} \approx 56\ \mathrm{mi/h}$$

Question 2

Usain Bolt ran 100 meters in 9.58 seconds. What was his average speed in miles per hour?

Accepted Answer

$$\displaystyle 10.44\ \mathrm{m/s} 	imes \frac{1\ \mathrm{mi}}{1609\ \mathrm{m}} 	imes \frac{3600\ \mathrm{s}}{1\ \mathrm{h}} \approx 23.4\ \mathrm{mi/h}$$

Question 3

A student walks 60 m from the library to the cafeteria, stopping for 1 minute halfway to talk to a friend. If the walking speed is $$1.5\ \mathrm{m/s}$$, what is the average speed for the entire trip?

Accepted Answer

$$\displaystyle \frac{60\ \mathrm{m}}{100\ \mathrm{s}} = 0.6\ \mathrm{m/s}$$

Question 4

Convert a speed of $$55.0\ \mathrm{mi/h} to $$meters per second.

Accepted Answer

$$\displaystyle 24.6\ \mathrm{m/s}$$

Question 5

If 8 billion people stood on the equator, each separated by 2 meters, how many times would the line of people circle the Earth? (Earth's equator $$= 40,000\ \mathrm{km})$$

Accepted Answer

$$\displaystyle \frac{16 	imes 10^9$\ \mathrm{m}}{4 	imes 10^7$\ \mathrm{m}} = 400$$

Question 6

A car travels at a constant speed of $$55\ \mathrm{mi/h}$$ for a distance of $$215\ \mathrm{mi}. $$How long does the trip take?

Accepted Answer

$$\displaystyle \frac{215\ \mathrm{mi}}{55\ \mathrm{mi/h}} \approx 3.9\ \mathrm{h}$$

Question 7

Which equation correctly describes the position $$x of an $$object moving at constant velocity $$v$$ along the $$x-$$axis, starting from $$x_0 at$$ $$t=0$$?

Accepted Answer

$$\displaystyle x = x_0$ + vt$$

Question 8

The period $$T of a $$pendulum of length $$l is $$given by $$T = 2\pi\sqrt{l/g}. $$What is the period for a pendulum of length $$2\ \mathrm{m}$$, using $$g = 9.8\ \mathrm{m/s^2$}$$?

Accepted Answer

$$\displaystyle 2\pi\sqrt{2/9.8} \approx 2.84\ \mathrm{s}$$

Question 9

During a 90-degree swing, a pendulum of length $$2\ \mathrm{m}$$ travels a distance equal to a quarter of the circumference of a circle. What is this distance?

Accepted Answer

$$\displaystyle \frac{1}{4} 	imes 2\pi 	imes 2\ \mathrm{m} = \pi\ \mathrm{m}$$

Question 10

Which of the following best defines instantaneous speed?

Accepted Answer

The speed of an object at a specific moment, as shown by a speedometer.

Question 11

Given $$x = kt^2$, what is the instantaneous velocity v$ at time t$?

Accepted Answer

$$\displaystyle v = \frac{dx}{dt} = 2kt$$

Question 12

A graph shows a five-leg journey with periods of rest and movement at constant speed. If the total distance is $$900\ \mathrm{m}$$ and the total time is $$26\ \mathrm{min}$$, what is the average speed in km/h?

Accepted Answer

$$\displaystyle \frac{900\ \mathrm{m}}{26\ \mathrm{min}} 	imes \frac{60\ \mathrm{min}}{1000\ \mathrm{m}} = 2.1\ \mathrm{km/h}$$

Question 13

Which of the following is the correct definition of the derivative for velocity at a point $$A$$?

Accepted Answer

$$\displaystyle v_A = \lim_{\Delta t 	o 0} \frac{\Delta x}{\Delta t}$$

Question 14

If a person counts $$37.2 	imes 10$$^{12}$$ dollars in 100 $$bills$$, one bill per second, how many years would it take?

Accepted Answer

$$\displaystyle \frac{37.2 	imes 10$$^{12}$$}{100} \div (60 	imes 60 	imes 24 	imes 365) \approx 11,800\ \mathrm{years}$$

Question 15

Which formula gives the average velocity $$\bar{v}$$ between two points $$x_i$$ and $$x_f at $$times $$t_i$$ and $$t_f$$?

Accepted Answer

$$\displaystyle \bar{v} = \frac{x_f - x_i}{t_f - t_i}$$

Question 16

A pendulum of length $$l$$ swings by $$90^\circ. $$What is the average speed of the sphere attached to the lower end during one period, given $$g = 9.8\ \mathrm{m/s^2$}$$ and $$l = 2\ \mathrm{m}$$?

Accepted Answer

$$\displaystyle \bar{v} = 0.5 \sqrt{9.8\ \mathrm{m/s^2$}} 	imes 2\ \mathrm{m} \approx 2.2\ \mathrm{m/s}$$

Question 17

Which of the following is the correct definition of the integral for total distance $$X$$ passed by a body from $$t_1 to$$ $$t_N$$?

Accepted Answer

$$\displaystyle X = \int_{t_1$}^{t_N} v(t)\,dt$$

Study Notes: Motion at a Constant Speed and Kinematics Fundamentals

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