Engineering Math

How many significant figures does each of the following numbers have?

a) 310

b) 0.00310

c) 1.031

d) 3.10×10⁵

Solution:

Part a

Zeroes before the decimal point merely locate the decimal point and are not significant. Thus, 310 has 2 significant figures.

Part b

Trailing zeros after the decimal point are significant because they indicate increased precision. Therefore, 0.00310 has 3 significant figures.

Part c

Zeroes between nonzero digits are significant. Therefore, 1.031 has 4 significant figures.

Part d

Just like in part b, trailing zeros after the decimal point are significant because they indicate increased precision.Therefore, 3.10×10⁵ has 3 significant figures.

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Physics for Scientists and Engineers 3rd Edition by Randall Knight, Chapter 1 Exercise and Problems 3

You’re driving along the highway at 60 mph until you enter a town where the speed limit is 30 mph. You slow quickly, but not instantly, to 30 mph. Draw a basic motion diagram of your car, using images from the movie, from 30 s before reaching the city limit until 30 s afterward.

Physics for Scientists and Engineers 3rd Edition by Randall Knight, Chapter 1 Exercise and Problems 2

A rocket is launched straight up. Draw a basic motion diagram, using the images from the movie, from the moment of liftoff until the rocket is at an altitude of 500 m.

Physics for Scientists and Engineers 3rd Edition by Randall Knight, Chapter 1 Exercise and Problems 1

A car skids to a halt to avoid hitting an object in the road. Draw a basic motion diagram, using the images from the movie, from the time the skid begins until the car is stopped.

Physics for Scientists and Engineers 3rd Edition by Randall Knight, Chapter 1 Conceptual Question 8

Determine the signs (positive or negative) of the position, velocity, and acceleration for the particle in Figure Q1.8.

Physics for Scientists and Engineers 3rd Edition by Randall Knight, Chapter 1 Conceptual Question 7

Determine the signs (positive or negative) of the position, velocity, and acceleration for the particle in Figure Q1.7.

Physics for Scientists and Engineers 3rd Edition by Randall Knight, Chapter 1 Conceptual Question 6

Determine the signs (positive or negative) of the position, velocity, and acceleration for the particle in Figure Q1.6.

Physics for Scientists and Engineers 3rd Edition by Randall Knight, Chapter 1 Conceptual Question 5

Does the object represented in Figure Q1.5 have a positive or negative value of $\displaystyle a_y$ ? Explain.

Physics for Scientists and Engineers 3rd Edition by Randall Knight, Chapter 1 Conceptual Question 4

Does the object represented in Figure Q1.4 have a positive or negative value of $\displaystyle a_x$ ? Explain.

Physics for Scientists and Engineers 3rd Edition by Randall Knight, Chapter 1 Conceptual Question 3

Is the particle in FIGURE Q1.3 speeding up? Slowing down? Or can you tell? Explain.

Solution:

Physics for Scientists and Engineers 3rd Edition by Randall Knight, Chapter 1 Conceptual Question 2

How many significant figures does each of the following numbers have?

a) 310

b) 0.00310

c) 1.031

d) 3.10×10⁵

Solution:

You’re driving along the highway at 60 mph until you enter a town where the speed limit is 30 mph. You slow quickly, but not instantly, to 30 mph. Draw a basic motion diagram of your car, using images from the movie, from 30 s before reaching the city limit until 30 s afterward.

A rocket is launched straight up. Draw a basic motion diagram, using the images from the movie, from the moment of liftoff until the rocket is at an altitude of 500 m.

A car skids to a halt to avoid hitting an object in the road. Draw a basic motion diagram, using the images from the movie, from the time the skid begins until the car is stopped.

Determine the signs (positive or negative) of the position, velocity, and acceleration for the particle in Figure Q1.8.

Determine the signs (positive or negative) of the position, velocity, and acceleration for the particle in Figure Q1.7.

Determine the signs (positive or negative) of the position, velocity, and acceleration for the particle in Figure Q1.6.

Does the object represented in Figure Q1.5 have a positive or negative value of ? Explain.

Does the object represented in Figure Q1.4 have a positive or negative value of ? Explain.

Is the particle in FIGURE Q1.3 speeding up? Slowing down? Or can you tell? Explain.

Solution:

How many significant figures does each of the following numbers have?

a) 310

b) 0.00310

c) 1.031

d) 3.10×105

Solution:

Does the object represented in Figure Q1.5 have a positive or negative value of $\displaystyle a_y$ ? Explain.

Does the object represented in Figure Q1.4 have a positive or negative value of $\displaystyle a_x$ ? Explain.

d) 3.10×10⁵