SPH 3U1
K/U -
Problem Set 1 : Kinematics
/48
T/I - /43
Com-
/10
Apps-
/24
Name: _______________________________________________
Communications Rubric
Level 0
0-49%
Level 1
50-59
Level 2
60-69 %
Level 3
70-79%
• Significant digits not used
• Grasp/Grams not followed
• Solution are not logical or
easy to follow
• Questions are done out of
order
• Solutions are not neat
• Units often ignored
• Significant digits often forgotten
• Grasp/Grams forgotten most
of the time
• Solutions are not easy to follow
• Questions are out of order and
many not attempted
• Solutions lack neatness
• Units used inconsistently
• Significant digits used
occasionally
• Grasp/Grams used occasionally
• Solution is logical and
somewhat easy to follow
• Questions are done in
order
• Solutions are neat
• Units properly used occasionally
Level 4
80-100%
• Significant digits used most
of the time
• Grasp/Grams used most of
the time
• Solutions are logical and
easy to follow most of the
time
• Questions are done in order
• Solutions are neat
• Units properly used most of
the time
• Significant digits used extensively
• Grasp/Grams used extensively
• Solution are logical and easy
to follow
• Questions are done in order
• Solutions are neat and easy to
read
• Units thoroughly and consistently used
Knowledge/Understanding (48 marks)
1. 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 person’s average velocity? Assume that vectors in the easterly
direction are (+), and those in the westerly direction are (–). Convert your answer from km/h to m/s. (4)
2. 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 car’s
average velocity. Convert your answer from km/h to m/s. (4)
3. Using the graph, determine the average velocity for these intervals. Show all work in correct form.
(a) AB (1)
(b) AD (1)
(c) BD (1)
4. A cart, starting from rest, slides down an inclined air-track and passes certain positions (d) in the time shown
(t). Using graphing techniques, show that the cart travels with uniform acceleration, and determine the value
of the acceleration in m/s2
d (cm)
t (s)
0
0
12.8
0.8
20.0
1.0
28.8
1.2
39.2
1.4
51.2
1.6
64.8
1.8
(10)
5. 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. (3)
6. Using the graph, determine each of the following.
(a) the average velocity for the first 2.5 s (1)
(b) the average velocity for the interval 2.5 to 7.5 s (1)
(c) the instantaneous velocity at the points A, B, and C (3)
(d) the times at which the instantaneous velocity is approximately zero (1)
7. From this graph determine the acceleration for each interval. Show all work in correct form. (5)
8. From this velocity-time graph, determine each of the following.
(a) the acceleration at any instant in the first 12 s (1)
(b) the instantaneous acceleration at (i) t = 25 s and (ii) t = 40 s (2)
(c) the average acceleration for the intervals (i) t = 0 to t = 25 s and (ii) t = 30 s to t = 50 s (2)
9. This graph below 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 object’s displacement in the first 3.0 s (2)
(b) the object’s displacement between t = 3.0 s and t = 5.0 s (1)
(c) the total displacement of the object in 14 s (2)
(d) the average velocity of the object from t = 0 to t = 8.0 (3)
Thinking/Inquiry (43 marks)
10. From the v-t graph below, draw the corresponding d-t graph and a-t graph. (Assume that d1 = 0.)
(8)
11. An executive jet cruises at 700 km/h. If the winds are light, it consumes kerosene at the rate of 38.0 L/min. If
the jet’s fuel tanks contain 6840 L when full, what is its maximum range? (2)
12. A train travels 58 km at an average velocity of 77 km/h [E], waits for 5.0 min at a station, and then runs for
half an hour at an average velocity of 64 km/h [E]. Find the following:
(a) the total displacement of the train (2)
(b) the average velocity for the whole trip (2)
13. A ball rolls along the floor, up a sloping board, and then back down the board and across the floor again. The
graph below represents this motion.
(a) At what time is the ball at its highest point? (1)
(b) What was the acceleration when the ball was (i) rolling up the board, (ii) rolling down the board, and (iii)
at rest at the top point? (2)
(c) How far up the board did the ball go? (1)
(d) What was the total displacement of the ball over the 9.0 s trip? (1)
14. Here is a v-t graph of two cars, A and B. At t = 0 s, A and B pass each other.
(a) Determine the acceleration of B during the final 3.0 s. (1)
(b) Find the distance between A and B at t = 5.0 s. (2)
(c) Find the average velocity of A in the first 5.0 s. (2)
(d) Find the instantaneous acceleration of A at t = 7.0 s. (1)
(e) Plot an acceleration-time graph for both A. Assume that any changes in acceleration occur
instantaneously. (3)
15. The below describes the motion of a capsule carried on a rocket fired vertically upward. The rocket ejected
the capsule at its highest point. The capsule fell freely with the rocket until its parachute opened at t = 300 s.
(a) At what time did the rocket reach its highest altitude? (1)
(b) What was the maximum altitude of the rocket? (3)
(c) What was the acceleration of the rocket during (i) the first stage and (ii) the second stage? (2)
(d) What was the average acceleration of the capsule during the interval t = 100 s to t = 300 s? (1)
(e) What was happening during the period t = 300 s to t = 400 s? (1)
(f) What was the terminal velocity of the capsule just before “splashdown”? (1)
16. The graph below represents the motion of an object over a recorded time interval. Using methods of graphical
analysis wherever possible, determine
(a) the object’s displacement relative to its starting position at t = 6.0 s. (2)
(b) the object’s average velocity between t = 0.0 s and t = 6.0 s. (1)
(c) the object’s average speed between t = 0.0 s and t = 6.0 s. (1)
(d) Including t = 0.0 s, how many times during the entire recorded time interval is the object at its starting
position? (1)
(e) During which interval is the object’s acceleration the greatest? What is the value of the acceleration during
this interval? (1)
Applications (24 marks)
17. Sketch the position-time graphs from the following graphs. (4)
18. Sketch the velocity-time graphs from the following position-time graphs. (6)
19.
Sketch the acceleration time graphs from the following velocity-time graphs. (2)
20.
Explain how GPS satellite operate. Include sufficient detail to receive full marks. Explain 4 other uses of GPS
satellites as well. (6)
21.
Think of a career related to physics that interest you. What do you find interesting about this career? How
would an understanding of kinematics be beneficial in the career that you have selected? (2)
22.
When the velocity is constant, can the average velocity over any time interval differ from the instantaneous
velocity at any instant? If so, give an example, if not, explain why? (2)
23.
Can an object be increasing in speed as its acceleration decreases? If so, give an example, if not, explain why. (2)
24.
Can the velocity of an object be negative when its acceleration is positive? What about vice versa? (2)