Question

1. the cross - country team goes on a 10 - mile run after school. they end the run outside of the locker room, where they started. find the distance and displacement of the runners.
2. a family travels 110 km east to spend the night in a hotel. the next day they drive back home, but after travelling 45 km west they decide to stop and visit with friends for the night. find the distance and displacement of the family.
3. a car drives 215 km west and then 85 km south. find the distance and displacement of the car.
4. if you ran 3.1 miles in 0.5 hours, what was your speed?
5. sound travels at 330 m/s. if a lightning bolt strikes the ground 5 m away from you, how long will it take for the sound of the strike to reach you?
6. a man drives south to work every day. if his 55 mile commute usually takes 0.75 hours, what is his average velocity?
7. a car travels at a constant speed of 30.0m/s for 0.80 h. find the total distance traveled in km.
8. sketch the following distance vs. time graphs (you will need 4): (label the graph)

a. an object not moving
b. an object moving at a constant speed
c. an object speeding up
d. an object slowing down
create a graph to show the progress of a runner who runs a 1 - km race in 3 minutes. the runner gets off to a fast start, runs the middle of the race at a more moderate pace, and then sprints to the finish.

Explanation:

1.

Step1: Define distance and displacement for cross - country team

Distance is total path length, displacement is straight - line distance from start to end. Team runs 10 miles and returns to starting point.
Distance = 10 miles, Displacement = 0 miles

2.

Step1: Calculate distance for family

Distance is sum of distances traveled. They travel 110 km east and 45 km west. Distance = 110 + 45=155 km

Step2: Calculate displacement for family

Displacement is net distance from start. 110 km east and 45 km west, so Displacement = 110 - 45 = 65 km east

3.

Step1: Calculate distance for car

Distance is sum of distances of two parts of journey. Distance = 215+85 = 300 km

Step2: Calculate displacement for car

Use Pythagorean theorem. Displacement $d=\sqrt{215^{2}+85^{2}}=\sqrt{46225 + 7225}=\sqrt{53450}\approx231$ km

4.

Step1: Use speed formula

Speed $v=\frac{d}{t}$, where $d = 3.1$ miles and $t = 0.5$ hours. $v=\frac{3.1}{0.5}=6.2$ miles per hour

5.

Step1: Use time formula

Time $t=\frac{d}{v}$, where $d = 5$ m and $v = 330$ m/s. $t=\frac{5}{330}=\frac{1}{66}\approx0.015$ s

6.

Step1: Use average velocity formula

Average velocity $v=\frac{d}{t}$, where $d = 55$ miles south and $t = 0.75$ hours. $v=\frac{55}{0.75}=\frac{220}{3}\approx73.3$ miles per hour south

7.

Step1: Convert time to seconds

$t=0.80$ h = 0.80×3600 s = 2880 s

Step2: Calculate distance in meters

Distance $d=v\times t$, where $v = 30.0$ m/s and $t = 2880$ s. $d=30\times2880 = 86400$ m

Step3: Convert distance to km

$d = 86.4$ km

8.

a.

For an object not moving, distance doesn't change with time. Graph is a horizontal line.

b.

For an object moving at a constant speed, distance - time graph is a straight line with a non - zero slope.

c.

For an object speeding up, the slope of the distance - time graph increases with time.

d.

For an object slowing down, the slope of the distance - time graph decreases with time.
For the 1 - km race in 3 minutes: Start with a steep slope for fast start, then a less steep slope for moderate pace, and then a very steep slope for sprint to finish.

Answer:

1. Distance: 10 miles, Displacement: 0 miles
2. Distance: 155 km, Displacement: 65 km east
3. Distance: 300 km, Displacement: approximately 231 km
4. 6.2 miles per hour
5. Approximately 0.015 s
6. Approximately 73.3 miles per hour south
7. 86.4 km

8.
a. Horizontal line
b. Straight line with non - zero slope
c. Graph with increasing slope
d. Graph with decreasing slope
For 1 - km race: Start with steep slope, then less steep, then very steep slope.