The Kinematics Challenge!

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14 Νοε 2013 (πριν από 3 χρόνια και 6 μήνες)

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The Kinematics Challenge!


1.

A woman and her dog are out for a morning run to the river, which is located 4.0 km away. The
woman runs at 2.5 m/s in a straight line. The dog is unleashed and runs back and forth at 4.5 m/s
between his owner and the river, unti
l she reaches the river. What is the total distance run by the dog?


2.

A car makes a 60 km trip with an average velocity of 40.0 km/h in a direction due north. The trip
consists of three parts. The car moves with a constant velocity of 25 km/h [N] for the f
irst 15 km and
62 km/h [N] for the next 32 km. With what constant velocity does the car travel for the last 13 km
segment of the trip?


3.

A locomotive is accelerating at 1.6 m/s
2
. It passes through a 20.0 m wide crossing in a time of 2.4 s.
After the locomot
ive leaves the crossing, how much time is required until its speed reaches 32 m/s?


4.

In the 100
-
m dash a sprinter accelerates from rest to a top speed with an acceleration whose magnitude
is 2.68 m/s
2
. After achieving top speed, he runs the remainder of the

race without speeding up or
slowing down. If the total race in run in 12.0 s, how far does he run during the acceleration phase?


5.

A roof tile falls from rest from the top of a building. An observer inside the building notices that it
takes 0.20 s for the
tile to pass her window, whose height is 1.6 m. How far above the top of the
window is the roof?


6.

A dog sees a flowerpot sail up and then ba
ck down past a window which is 1.47m

high. If the total
time the pot is in sight is 1.0 s, find the height above the

window the pot rises.


7.

Suppose the first one
-
fourth of the distance between two points is covered with an average velocity of
+18 m/s. The average velocity for the remainder of the trip is +51 m/s. What is the average velocity for
the entire trip?


8.

A trai
n has a length of 92 m and starts from rest with a constant acceleration at t = 0. At this instant, a
car just reaches the end of the train. The car is moving with a constant velocity. At t = 14 s, the car
reaches the front of the train. Ultimately, howeve
r, the train pulls ahead of the car, and at a time t = 28
s, the car is again at the rear of the train. Find the magnitude of (a) the car’s velocity and (b) the train’s
acceleration.


9.

A commuter train can minimize the time
t

between two stations by acceler
ating (a
1

= 0.1 m/s
2
) for a
time
t
1
, then undergoing a negative acceleration (a
2

=
-
0.5 m/s
2
) by using his brakes for a time
t
2
. Since
the stations are only 1 km apart, the train never reaches its maximum velocity. Find the minimum time
of travel
t
, and th
e time
t
1
.


10.

Suppose you adjust your garden hose nozzle for a hard stream of water. You point the nozzle vertically
upward at a height of 1.5 m above the ground. When you quickly move the nozzle away from the
vertical, you hear the water striking the ground

next to you for 2.0 s. What is the water speed as it
leaves the nozzle?


11.

***In 1987, Art Boileau won the Los Angeles Marathon, 26 mi and 385 yds, in 2 h, 13 min, and 9 s.
At the 21
-
mi marker, Boileau had a 2.50
-
min. lead on the second place winner, who
later crossed the
finish line 30 s after Boileau. Assume that Boileau maintained one constant average speed during the
race and that both runners had been running at the same speed when Boileau passed the 21
-
mi marker.
Find the average acceleration (in m/s
2
) that the second place contestant had during the remaining part
of the race after Boileau passed the 21
-
mi marker.



Answers:
(1)
7.2x10
3

m,
(2)

34 km/h [N],
(3)

14 s,
(4)

18 m,
(5)

2.5 m,
(6)

0.012 m
,
(7)

+35 m/s,
(8)

a.13
m/s, b. 0.93 m/s
2
,
(9)

155 s,
129 s
, (10) 9.1 m/s [up], (11) 5.86x10
-
4

m/s
2