SPH3U - Koblbauer's Math Site
SPH3U Kinematics Unit Assignment Name: _______________
1. A camper kayaks 13 km [E] from a camping site, stops, has lunch, and then paddles 20 km [W]. What is his final position with reference to the camping site?
2. A canoeist paddles 4.0 km [E], 5.0 km [W], and 6.0 km [S]. Draw position vectors to represent this scenario. What is her final position with reference to where she started?
3. Starting from his home, a student cycles 200 m [W], 100 m [S], and 500 m [S 30° E] to school. Draw position vectors to represent this scenario. What distance does he travel to school? What is his displacement?
4. A cyclist covers 20 km [W] in 1.5 h and then 15 km [S] in 2.0 h to reach the finish line. Calculate her average speed and average velocity.
5. An ice cream truck moves 500 m [E] in 10 min, 400 m [W] in the next 10 min, and 300 m [N] in the next 5 minutes. Calculate the average speed and average velocity of the ice cream truck.
6. Which of the following describe uniform motion?
(a) a child on a merry-go-round
(b) a ball rolling down a ramp
(c) a car driving west at 100 km/h
7. Sketch a position-time graph for a student who is (a) walking home with a constant positive velocity (b) stopping at the mall 5 km from home (c) cycling to school with constant velocity.
8. Please refer to the diagram on the right to answer the following.
(a) Describe briefly the kind of motion that is
taking place in each lettered stage of the
situation represented by the position-time graph.
(b) When is the object at a position of 20.0 m?
(c) How far is the object from the starting point after 20 s?
(d) What is the object’s velocity during each of the lettered intervals?
(e) Calculate the average velocity for the 40-s to 120-s time interval.
(f) With reference to its position at 20.0 s, when is the object’s average velocity zero?
9. A van is moving east at 80 km/h when the driver sees a problem ahead and within 5.0 s slows down to 50 km/h. Calculate the acceleration of the van in km/h/s and in m/s2.
10. A runner takes 0.123 s to get off the blocks after the starting signal. She rapidly accelerates to top speed. Velocity-time data for the first six seconds of the race is shown in the table.
Time (s) |0 |0.123 |0.50 |1.00 |1.50 |2.0 |3.0 |4.0 |5.0 |6.0 | |Velocity (m/s [forward]) |0 |0 |2.4 |4.8 |6.6 |8.2 |10.5 |11.8 |12.0 |12.0 | |
(a) Calculate her average acceleration between ∆t = 0.123 s and ∆t = 0.50 s.
(b) Calculate her average acceleration between ∆t = 3.0 s and ∆t = 4.0 s.
(c) What happened to her acceleration over the first five seconds?
(d) What is her acceleration in the 5-s to 6-s time interval?
11. Sketch a position-time graph and a velocity-time graph for constant velocity.
12. Sketch a position-time graph and a velocity-time graph for constant acceleration.
13. Please refer to the diagram on the right to
answer the following.
(a) What is the velocity during each lettered interval?
(b) Draw a corresponding velocity-time graph.
14. Please refer to the diagram below to calculate each of the following:
(a) acceleration during each interval
(b) displacement during each interval
(c) final position of the object
15. A cat moving at a velocity of 7.0 m/s [N] accelerates uniformly in 4.0 s to 13 m/s [S]. What is the cat’s average velocity?
16. A jackal travelling at its top velocity of 16 m/s [W] slows down uniformly to a velocity of 4.0 m/s [W] in 5.0 s. What is the displacement of the jackal during this time?
17. An elk moving at a velocity of 18 km/h [N] accelerates at 1.5 m/s2 [N]. How long will it take the elk to reach its top velocity of 72 km/h [N]?
18. A skier is moving down a uniform slope at 2.0 m/s. If the acceleration down the hill is 3.0 m/s2, find the skier’s displacement after 6.0 s.
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