Practice 2A: | 1
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**Average velocity and displacement
- by the dynamic duo, Lisa and Heather Jacobson, 2005**

**1. Heather and Matthew walk eastward with a speed of 0.98
m/s. If it takes them 34 min to walk to the store, how far have they
walked? **

Here's what you know, Dt = (34
min)(60 sec/min) = 2040 sec, and v_{avg} = 0.98 m/s. Use the
formula v_{avg} = Dx/Dt and plug in: 0.98 m/s = Dx/2040 sec, so Dx = (0.98m/s)(2040 s) = 1999.2 m = **2.0 km** (1000 m = 1 km)

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**2. If Joe rides south on his bicycle in a straight line
for 15 min with an average speed of 12.5 km/h, how far has he ridden? **

First rearrange the average velocity formula to solve for displacement: v_{avg} = Dx/Dt becomes
Δx = v_{avg} Δt . You know that v_{avg }= 12.5
km/h, and
Δt = (15min)(1h/60min) = .25 h, so Δx = (12.5km/h)(.25h) = **3.1 km**

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**3. It takes you 9.5 min to walk with an average velocity
of 1.2 m/s to the north from the bus stop to the museum entrance. What is your
displacement? **

Using the same formula as in problem 2, plug in the values you know: v_{avg
}= 1.2 m/s and Dt =
(9.5min)(60sec/min) = 570sec. So Δx = (1.2m/s)(570s) = 684m = **680 m** (sig figs)

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**4. Simpson drives his car with an average velocity of 48.0
km/h to the east. How long will it take him to drive 144 km on a straight
highway?**

This time rearrange the average
velocity formula to solve for time: v_{avg} = Dx/Dt becomes
Dt = Dx/ v_{avg , }so Dt
= (144km)/(48.0 km/h) = **3 h**

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**5. Look back at item 4. How much time would Simpson save
by increasing his average velocity to 56.0 km/h to the east? **

This is the same process as problem 4, only with a different average
velocity. Dt = Dx/
v_{avg }= (144km)/(56.0 km/h)
=2.57 h. The question asks for the time saved, which would be the difference
between the time in problem 4 and the time in problem 5. So time saved = 3h –
2.57h = **.43 hours saved**

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**6. A bus travels 280 km south along a straight path with
an average velocity of 88 km/h to the south. The bus stops for 24 min, then it
travels 210 km south with an average velocity of 75 km/h to the south.
a. How long does the total trip last?
b. What is the average velocity for the total trip? **

a. Okay, to find the total time split the trip into three parts and solve
for time in each. Then add the three parts together to find the total
time.
part 1: Dt = Dx/ v_{avg }= (280km)/(88km/h) = 3.182 h part 2: Dt =
(24min)(1h/60min) = .4 h
part 3: Dt = Dx/ v_{avg }= (210km)/(75km/h) = 2.8 h total
time = 3.182 h + .4 h + 2.8 h = **6.38
h or 6 h 23 min**

b. To find the average velocity of the total trip, use the formula v_{avg}
= Dx/Dt
, and for Dx and Dt use the time and displacement of the total
trip. v_{avg }=
(280km + 210km)/(6.38h) = **77 km/h**

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