motion • guided reading and study
describing and measuring motion (continued)
3. an object is in motion if it changes position relative to a(n)
4. complete the table about si
si
question | answer
what is its whole name? |
is its basic unit of length? |
does the prefix milli- |
5. how many centimeters are there in a meter?
6. how many meters are there in a kilometer?
calculating speed (pp. 10–11)
7. what is the formula used to calculate the speed of an object?
8. how would you find the average speed of a cyclist throughout an entire race?
describing velocity (pp. 12–13)
9. speed in a given direction is called __________
10. an approaching storm is moving at 15 km/hr. what do you need to know to determine its velocity?
graphing motion (pp. 14–15)
11. the slant of a line on a graph is called its __________
12. is the following sentence true or false? the steepness of a distance-versus-time graph’s slope depends on how quickly or slowly the object is moving.

Question

Accepted Answer

### Question 5: How many centimeters are there in a meter?
# Explanation:
## Step1: Recall the metric system prefixes and conversions. The centi- prefix means $10^{-2}$, so 1 centimeter ($	ext{cm}$) is $0.01$ meters ($	ext{m}$). To find how many centimeters are in 1 meter, we can set up the conversion: let $x$ be the number of centimeters in 1 meter. Then $1\ 	ext{m} = x\ 	ext{cm}$, and since $1\ 	ext{cm} = 0.01\ 	ext{m}$, we can solve for $x$ by dividing 1 by 0.01.
$$x=\frac{1\ 	ext{m}}{0.01\ 	ext{m/cm}} = 100$$
# Answer: 100

### Question 6: How many meters are there in a kilometer?
# Explanation:
## Step1: Recall the metric system prefixes. The kilo- prefix means $10^{3}$, so 1 kilometer ($	ext{km}$) is $1000$ meters ($	ext{m}$). By definition, the conversion from kilometers to meters is that 1 km equals 1000 m.
# Answer: 1000

### Question 7: What is the formula used to calculate the speed of an object?
# Explanation:
## Step1: Recall the definition of speed. Speed is defined as the distance traveled by an object divided by the time taken to travel that distance. If we let $s$ represent speed, $d$ represent distance, and $t$ represent time, the formula is derived from this definition.
$$s = \frac{d}{t}$$
# Answer: $s=\frac{d}{t}$ (where $s$ is speed, $d$ is distance, and $t$ is time)

### Question 8: How would you find the average speed of a cyclist throughout an entire race?
# Explanation:
## Step1: Recall the concept of average speed. Average speed is the total distance traveled divided by the total time taken. For a cyclist in a race, we need to determine the total distance of the race (let's call it $D$) and the total time the cyclist took to complete the race (let's call it $T$).
## Step2: Apply the average speed formula. Using the formula for average speed, which is the same as the speed formula but with total distance and total time, we have average speed $=\frac{	ext{total distance}}{	ext{total time}}=\frac{D}{T}$.
# Answer: Divide the total distance of the race by the total time the cyclist took to complete the race (i.e., average speed $=\frac{	ext{total distance}}{	ext{total time}}$)

### Question 9: Speed in a given direction is called __________
# Brief Explanations:
In physics, when speed is associated with a direction, it is defined as velocity. Speed is a scalar quantity (magnitude only), while velocity is a vector quantity (magnitude and direction). So speed with a given direction is velocity.
# Answer: velocity

### Question 10: An approaching storm is moving at 15 km/hr. What do you need to know to determine its velocity?
# Brief Explanations:
Velocity is a vector quantity that includes both speed (magnitude) and direction. The storm's speed is given as 15 km/hr, so to find its velocity, we need to know the direction in which the storm is moving (e.g., north, south - east, etc.).
# Answer: The direction in which the storm is moving (e.g., north, south - east, etc.)

### Question 11: The slant of a line on a graph is called its __________
# Brief Explanations:
In graphing, the slant of a line (the steepness or the rate of change of the line) is called the slope. The slope of a line on a graph (e.g., a distance - time graph or a velocity - time graph) is calculated as the ratio of the change in the vertical axis (rise) to the change in the horizontal axis (run).
# Answer: slope

### Question 12: Is the following sentence true or false? The steepness of a distance - versus - time graph’s slope depends on how quickly or slowly the object is moving.
# Brief Explanations:
In a distance - time graph, the slope is calculated as $\frac{	ext{change in distance}}{	ext{change in time}}$, which is the speed of the object. A steeper slope means a larger change in distance over a given change in time, which corresponds to a higher speed (the object is moving quickly). A less steep slope means a smaller change in distance over time, corresponding to a lower speed (the object is moving slowly). So the steepness of the slope (which is speed) depends on how quickly or slowly the object is moving.
# Answer: True

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Explanation:

Question 5: How many centimeters are there in a meter?

Step1: Recall the metric system prefixes. The kilo- prefix means $10^{3}$, so 1 kilometer ($\text{km}$) is $1000$ meters ($\text{m}$). By definition, the conversion from kilometers to meters is that 1 km equals 1000 m.

Step1: Recall the definition of speed. Speed is defined as the distance traveled by an object divided by the time taken to travel that distance. If we let $s$ represent speed, $d$ represent distance, and $t$ represent time, the formula is derived from this definition.

Answer:

Question 6: How many meters are there in a kilometer?