Practice 2A: | 1
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up
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 vavg = 0.98 m/s. Use the
formula vavg = 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: vavg = Dx/Dt becomes
Δx = vavg Δt . You know that vavg = 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: vavg
= 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: vavg = Dx/Dt becomes
Dt = Dx/ vavg , 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/
vavg = (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/ vavg = (280km)/(88km/h) = 3.182 h part 2: Dt =
(24min)(1h/60min) = .4 h
part 3: Dt = Dx/ vavg = (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 vavg
= Dx/Dt
, and for Dx and Dt use the time and displacement of the total
trip. vavg =
(280km + 210km)/(6.38h) = 77 km/h
(Table
of contents)