motion in a straight line
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Chapter 2 Motion in a Straight Line
Fundamentals of Physics: A Senior Course
SHORT ANSWER
1.State the displacement of each of the following changes in position.
(a) 8 km to 2 km
(b) +2 km to 8 km
(c) 0 km to +8 km
(d) 8 km to +20 km
(e) +8 km to 8 km
ANS:
(a)
(b)
(c)
(d)
(e)
There is a reference for this on page 43 of the FOP text.
REF:K/UOBJ:1.1LOC:FM1.02KEY:FOP 2.1, p.45
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2.The symbol D has other uses. Find the change in each of the following.
(a) The temperature falls from +10C to 20C. Find Dt.
(b) The value of a stock increases from $12.00 to $17.50. Find D$.
(c) A person on a diet goes from 60 kg to 55 kg. Express Dm.
(d) A ball falls from a point +20 m above the ground into a hole 10 m deep.
Find Dd.
ANS:
(a)
(b)
(c)
(d)
REF:K/UOBJ:1.1KEY:FOP 2.1, p.45
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3.What is the uniform velocity of an airplane that flies 602 m [E] in 2.50 s? Express your answer in metres per second, and kilometres per hour.
ANS:
REF:K/UOBJ:1.1LOC:FM1.02KEY:FOP 2.2, p.46
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4.The tine on a tuning fork moves 1.0 mm to the right in 4.0 103 s. What is the uniform velocity of the tine in metres per second?
ANS:
REF:K/UOBJ:1.1LOC:FM1.02KEY:FOP 2.2, p.46
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5.An electron travels at a uniform velocity of 1.30 105 m/s. How much time is required for a displacement of 1.00 m?
ANS:
REF:K/UOBJ:1.1LOC:FM1.02KEY:FOP 2.2, p.46
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6.A spaceship travelled at a uniform velocity of 3.2 104 km/h for 2.7 d. What was the displacement of the spaceship?
ANS:
REF:K/UOBJ:1.1LOC:FM1.02KEY:FOP 2.2, p.46
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7.Find the velocity in each section of the following position-time graph.
ANS:
REF:K/UOBJ:1.1LOC:FM1.02KEY:FOP 2.3, p.49
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8.A person walks 5.0 km towards the east in 2.00 h, then 1.5 km towards the west in 0.50 h, and finally 10.0 km towards the east again in 2.25 h. What is the persons average velocity? Assume that vectors in the easterly direction are (+), and those in the westerly direction are ().
ANS:
total displacement
total time
which, since it is positive, represents an average velocity towards the east.
REF:K/UOBJ:1.1LOC:FM1.02KEY:FOP 2.3, p.51
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9.A car is driven for 1.00 h with a velocity of 100 km/h towards the south, then for 0.50 h with a velocity of 50 km/h towards the north, and finally for 0.75 h with a velocity of 80 km/h towards the south. Find the cars average velocity.
ANS:
Let [N] be positive (+).
REF:K/UOBJ:1.1LOC:FM1.02KEY:FOP 2.3, p.51
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10.Find the average velocities for the intervals AB and BC.
ANS:
Interval AB
Interval BC
REF:K/UOBJ:1.1LOC:FM1.02KEY:FOP 2.3, p.51
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11.Using the graph, determine the average velocity for each of the following sections.
(a) t = 0 s to t = 2 s
(b) t = 6 s to t = 12 s
(c) t = 6 s to t = 15.5 s
ANS:
(a)
(b)
(c)
REF:K/UOBJ:1.1LOC:FM1.02KEY:FOP 2.4, p.52
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12.A hockey players slapshot averages 51.5m/s on its flight from the blue line to the goal, 20m away. How long does the puck take to reach the goal?
ANS:
REF:K/UOBJ:1.1LOC:FM1.02KEY:FOP 2.4, p.52
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13.Using the graph, determine the average velocity for these intervals.
(a) AB
(b) AD
(c) BD
ANS:
(a)
(b)
(c)
REF:K/UOBJ:1.1LOC:FM1.02KEY:FOP 2.4, p.52
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14.On the following position-time graph, find the instantaneous velocities at points A, B, and C by finding the slope of the tangent to the graph at each of the points.
ANS:
For point A:
For point B:
For point C:
REF:K/UOBJ:1.1LOC:FM1.02KEY:FOP 2.5, p.53
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15.Using the graph, determine each of the following.
(a) the average velocity for the first 2.5 s
(b) the average velocity for the interval 2.5 to 7.5 s
(c) the instantaneous velocity at the points A, B, and C
(d) the times at which the instantaneous velocity is approximately zero
ANS:
(a)
(b)
(c)
(d) The instantaneous velocity is approximately zero when the slope of the d-t graph is approximately zero. This occurs at t = 8.2s, 12.5s, 14.5s.
REF:K/UOBJ:1.1LOC:FM1.02KEY:FOP 2.5, p.54
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16.The following graph is that of an object moving in a straight line. East is considered as the positive direction.
(a) Determine the position of the object at t = 7.0 s.
(b) The graph shows five distinct sections. Briefly, and in general terms, describe the motion of the object in each of these sections.
(c) Considering the whole journey, calculate the average velocity.
(d) Find the instantaneous velocity at t = 13 s.
(e) Using an appropriate scale, draw a velocity-time graph from the position-time graph.
ANS:
(a) Position after 7.0 s is 10 m or 10 m [W].
(b) (i) t = 0 to t = 4.0 s
Uniform velocity of 2.5 m/s [W].
(ii) t = 0 to t = 7.0 s stopped.
(iii) t = 7.0 s to t = 9.0 s
Uniform velocity of 7.5 m/s [E].
(iv) t = 7.0 s to t = 11.0 s
Uniform velocity of approximately 1.3 m/s [W].
(v) t = 11.0 s to t = 14.0 s
Uniform acceleration in the easterly direction.
(c)
(d)
(e)
REF:K/UOBJ:1.1LOC:FM1.02KEY:FOP 2.6, p.56
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17.This graph describes the motion of an object moving in a straight line. At the beginning it is going east. From the graph determine each of the following.
(a) the objects displacement in the first 3.0 s
(b) the objects displacement between t = 3.0 s and t = 5.0 s
(c) the total displacement of the object in 14 s
(d) the average velocity of the object from t = 0 to t = 8.0
(e) the d-t graph; use it to check your answers to parts (a) to (d)
ANS:
(a)
(b) Displacement = 0 m
(c)
(d)
(e)