6/25/2016
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1D Kinematics #2 (7943245)
Question
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Question Details
OSColPhys1 2.1.002. [3203539]
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OSColPhys1 2.3.011. [2153212]
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Find the following for path C in the figure below.
(a) The distance traveled.
13 m
(b) The magnitude of the displacement from start to finish.
9 m
(c) The displacement from start to finish.
9 m
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Reading
2.
Question Details
A student drove to the university from her home and noted that the odometer on her car increased by 13.0 km. The trip
took 20.0 min.
(a) What was her average speed?
39 km/h
(b) If the straight-line distance from her home to the university is 10.3 km in a direction 25.0° south of east,
what was her average velocity?
30.9 km/h (25° S of E)
(c) If she returned home by the same path 7 h 30 min after she left, what were her average speed and velocity
for the entire trip?
average speed
3.47 km/h
average velocity
0 km/h
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Reading
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Question Details
OSColPhys1 2.8.065. [3203540]
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OSColPhys1 2.P.017.WA. [2707320]
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A graph of v(t) is shown for a world-class track sprinter in a 100-m race. (See figure below).
(a) What is his average velocity for the first 4 s?
6 m/s
(b) What is his instantaneous velocity at t = 6 s?
12 m/s
(c) What is his average acceleration between 0 and 4 s?
3 m/s2
(d) What is his time for the race?
10.3 s
Additional Materials
Reading
4.
Question Details
Suppose you are looking down from a helicopter at three cars traveling in the same direction along a freeway. The
positions of the three cars every 2 seconds are represented by dots on the diagram. The positive direction is to the right.
(a) Which car is traveling at a constant speed?
Car A
Car B
Car C
All cars are traveling at a constant speed.
None of the cars are traveling at a constant speed.
(b) During which time interval do Car A and Car B have the same average speed?
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t1 to t2
t2 to t3
t3 to t4
t4 to t5
(c) Which car has the greatest average velocity during the time interval t1 to t2?
Car A
Car B
Car C
(d) Which car has the greatest average velocity during the time interval t4 to t5?
Car A
Car B
Car C
(e) At which time does Car B catch up with Car A?
t2
t3
t4
t5
(f) During what time interval does Car C pass Car A?
t1 to t2
t2 to t3
t3 to t4
t4 to t5
(g) At what time does Car A catch Car C?
t2
t3
t4
t5
t6
(h) During what time interval does Car B pass Car C?
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t1 to t2
t2 to t3
t3 to t4
t4 to t5
(i) Which car has an acceleration in the positive direction?
Car A
Car B
Car C
(j) Which car has an acceleration in the negative direction?
Car A
Car B
Car C
Solution or Explanation
For parts (a) through (d), the key feature to look for is the size of the change in position within a time interval, which
means the size of the spacing between successive dots. Since velocity is the change in position per change in time, and
each successive dot is separated by an equal time interval, the magnitude of average velocity, or average speed, is larger
when there is larger spacing between successive dots. In part (a), Car A has spacing between dots that is the same for
each interval, so its speed is constant. In (b), Car A and Car B have equal spacing of 2 units between successive dots for
the interval from t2 to t3. This means they have the same average velocity over that interval. In (c), Car C's velocity is
larger than the other cars' from t1 to t2 because its spacing between the dots is largest (4 units). And in (d) Car B has the
largest spacing between the dots at t4 and t5, so its speed is largest during that interval.
For parts (e) through (h), simply compare the positions of the three cars at each successive point in time. In (e), Car B is
behind Car A until t4, at which time they are at the same position; at the next time Car B is ahead. In (f), Car C and Car A
are at the same position at t1, but Car C is ahead at t2. Later, as seen in part (g), Car A catches up to C again, as it is
behind C at t5, but at the same position at t6. For part (h), Car B is behind Car C up through t4, but ahead of Car C at t5.
In (i) and (j) we have to remember that acceleration is the change in velocity per change in time. On this diagram, as we
already discussed, velocity is indicated by the change in position between these equal time intervals. So for acceleration,
we need to look at how the spacing between dots is changing from one interval to the next. The spacing between intervals
does not change for Car A, indicating a zero acceleration (constant velocity); it gets larger with each interval for Car B,
indicating an acceleration in the positive direction; and it gets smaller for Car C, indicating an acceleration in the negative
direction.
Supporting Materials
Physical Constants
Additional Materials
Reading
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OSColPhys1 2.P.044.WA. [2707249]
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A child operates a remote controlled toy car on a linear track. The figure below plots the car's position as a function of
time.
Find the velocity of the toy car over the following time intervals. Indicate the direction with the sign of your answer.
(a) From 0 s to 2 s
1.5 m/s
(b) From 2 s to 4 s
-1.75 m/s
(c) From 4 s to 6 s
0 m/s
(d) From 6 s to 9 s
0.167 m/s
Solution or Explanation
Average velocity is defined as v = Δx/Δt, the change in position over change in time. For each segment of the graph,
calculate the change in x, the vertical axis, divided by the change in t, the horizontal axis. In other words, find the slope
of each segment. The sign of the slope indicates the direction of the velocity.
(a)
v=
3m−0m
= 1.5 m/s
2s−0s
(b)
v=
−0.5 m − 3 m
= −1.75 m/s
4s−2s
(c)
v=
−0.5 m − (−0.5 m)
= 0 m/s
6s−4s
(d)
v=
0 m − (−0.5) m
= 0.167 m/s
9s−6s
Supporting Materials
Physical Constants
Additional Materials
Reading
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Name (AID): 1D Kinematics #2 (7943245)
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