answer the following questions. make sure to show all work to receive credit. you may need a separate sheet of paper.
1. a student practicing for a track meet runs one 400-m lap in 55 seconds.
a. what was their average speed?
b. what was the average velocity?
2. a space shuttle orbits earth at a speed of 21,000 km/hr. how far will it have traveled in 1.5 hours?
3. a frightened mouse runs 50 cm to the right and then 70 cm to the left in 20 seconds.
a. what the mouse’s average speed?
b. what was the mouse’s average velocity?
4. a school bus moves at a speed of 35 mi/hr for 20 miles. how long will it take the bus to get to school?
5. a train takes 3.5 hours while moving at a speed of 120 mi/hr to make it to the next stop. how far apart are the train stations?
6. how long would it take for a car to travel 200 km if it has an average speed of 55 km/hr?

Question

answer the following questions. make sure to show all work to receive credit. you may need a separate sheet of paper.
1. a student practicing for a track meet runs one 400-m lap in 55 seconds.
   a. what was their average speed?
   b. what was the average velocity?
2. a space shuttle orbits earth at a speed of 21,000 km/hr. how far will it have traveled in 1.5 hours?
3. a frightened mouse runs 50 cm to the right and then 70 cm to the left in 20 seconds.
   a. what the mouse’s average speed?
   b. what was the mouse’s average velocity?
4. a school bus moves at a speed of 35 mi/hr for 20 miles. how long will it take the bus to get to school?
5. a train takes 3.5 hours while moving at a speed of 120 mi/hr to make it to the next stop. how far apart are the train stations?
6. how long would it take for a car to travel 200 km if it has an average speed of 55 km/hr?

Accepted Answer

### Question 1
#### Part A
# Explanation:
## Step1: Recall the formula for average speed
Average speed is calculated as total distance divided by total time, i.e., $ v_{avg}=\frac{d}{t} $.
## Step2: Identify the values of distance and time
The distance $ d = 400\space m $ and the time $ t = 55\space s $.
## Step3: Calculate the average speed
Substitute the values into the formula: $ v_{avg}=\frac{400}{55}\approx7.27\space m/s $ (rounded to two decimal places).
# Answer:
The average speed is approximately $ 7.27\space m/s $.

#### Part B
# Explanation:
## Step1: Recall the formula for average velocity
Average velocity is displacement divided by time. Displacement is the change in position. For a lap (a circular path), the starting and ending points are the same, so displacement $ \Delta x = 0\space m $.
## Step2: Calculate the average velocity
Using the formula $ \vec{v}_{avg}=\frac{\Delta x}{t} $, substitute $ \Delta x = 0\space m $ and $ t = 55\space s $. So $ \vec{v}_{avg}=\frac{0}{55}=0\space m/s $.
# Answer:
The average velocity is $ 0\space m/s $.

### Question 2
# Explanation:
## Step1: Recall the formula for distance
The formula relating speed ($ v $), time ($ t $) and distance ($ d $) is $ d = v\times t $.
## Step2: Identify the values of speed and time
The speed $ v = 21000\space km/hr $ and the time $ t = 1.5\space hr $.
## Step3: Calculate the distance
Substitute the values into the formula: $ d = 21000\times1.5 = 31500\space km $.
# Answer:
The space shuttle will travel $ 31500\space km $ in 1.5 hours.

### Question 3
#### Part A
# Explanation:
## Step1: Recall the formula for average speed
Average speed is total distance divided by total time, $ v_{avg}=\frac{d_{total}}{t} $.
## Step2: Calculate the total distance
The mouse runs $ 50\space cm $ to the right and $ 70\space cm $ to the left. So total distance $ d_{total}=50 + 70=120\space cm $. The time $ t = 20\space s $.
## Step3: Calculate the average speed
Substitute into the formula: $ v_{avg}=\frac{120}{20}=6\space cm/s $.
# Answer:
The mouse's average speed is $ 6\space cm/s $.

#### Part B
# Explanation:
## Step1: Recall the formula for average velocity
Average velocity is displacement divided by time. Displacement is the final position minus the initial position. Let the right be positive. Initial position $ x_i = 0\space cm $, final position $ x_f=50 - 70=- 20\space cm $ (since it moves 50 cm right and 70 cm left). So displacement $ \Delta x=x_f - x_i=-20 - 0=-20\space cm $.
## Step2: Calculate the average velocity
Using the formula $ \vec{v}_{avg}=\frac{\Delta x}{t} $, substitute $ \Delta x=-20\space cm $ and $ t = 20\space s $. So $ \vec{v}_{avg}=\frac{-20}{20}=- 1\space cm/s $. The negative sign indicates the direction is to the left.
# Answer:
The mouse's average velocity is $ - 1\space cm/s $ (or $ 1\space cm/s $ to the left).

### Question 4
# Explanation:
## Step1: Recall the formula for time
From $ v=\frac{d}{t} $, we can re - arrange it to $ t=\frac{d}{v} $.
## Step2: Identify the values of distance and speed
The distance $ d = 20\space miles $ and the speed $ v = 35\space mi/hr $.
## Step3: Calculate the time
Substitute the values into the formula: $ t=\frac{20}{35}=\frac{4}{7}\approx0.57\space hours $ (or $ \frac{4}{7}\times60\approx34.29\space minutes $).
# Answer:
It will take the bus approximately $ 0.57\space hours $ (or 34.29 minutes) to get to school.

### Question 5
# Explanation:
## Step1: Recall the formula for distance
The formula is $ d = v\times t $.
## Step2: Identify the values of speed and time
The speed $ v = 120\space mi/hr $ and the time $ t = 3.5\space hours $.
## Step3: Calculate the distance
Substitute the values into the formula: $ d = 120\times3.5 = 420\space miles $.
# Answer:
The train stations are 420 miles apart.

### Question 6
# Explanation:
## Step1: Recall the formula for time
From $ v=\frac{d}{t} $, we get $ t=\frac{d}{v} $.
## Step2: Identify the values of distance and speed
The distance $ d = 200\space km $ and the speed $ v = 55\space km/hr $.
## Step3: Calculate the time
Substitute the values into the formula: $ t=\frac{200}{55}=\frac{40}{11}\approx3.64\space hours $ (or $ \frac{40}{11}\times60\approx218.18\space minutes $).
# Answer:
It will take the car approximately $ 3.64\space hours $ (or 218.18 minutes) to travel 200 km.

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QUESTION IMAGE

Question

Explanation:

Question 1

Part A

Step1: Recall the formula for average speed

Step2: Identify the values of distance and time

Step3: Calculate the average speed

Step1: Recall the formula for average velocity

Step2: Calculate the average velocity

Step1: Recall the formula for distance

Step2: Identify the values of speed and time

Step3: Calculate the distance

Answer:

Part B