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SPH3U Kinematics – Review Problems 1. An electric train initially moving at 25 km/h accelerates to 35 km/h in 20s. Find the average acceleration in m/s2. 2. A car travels 58 km at an average velocity of 77 km/h [E], waits for 5.0 min. at a station, and then travels for half an hour at an average velocity of 64 km/h [E]. Find (a) the total displacement of the car, and (b) the average velocity for the whole trip. 3. Starting from rest a bobsled has a constant acceleration of 2.0 m/s2. a) How fast is it going after 5.0 s? b) How far has it travelled in 5.0 s? c) What is the average velocity in the first 5.0 s? d) How far has it travelled by the time its speed has reached 40 m/s? 4. The Easter bunny runs along a straight and narrow path with a constant speed of 25 m/s. He passes a sleeping tortoise, which immediately starts to chase the bunny with a constant acceleration of 3.0x10-3 m/s2. How long does it take the tortoise to catch the bunny? (Answer in hours.) 5. A person is walking with a constant acceleration along a straight ditch. He starts his stopwatch as he passes a fence post and notes that it takes him 10 s to reach a pine tree 10 m farther along the ditch. As he passes the pine tree, his speed is 1.2 m/s. How far was he from the fence post when he started from rest? 6. Two trains, one travelling at 100 km/h and the other at 128 km/h, are headed towards one another along a straight, level track. When the trains are 1.2 km apart, each engineer simultaneously sees the other’s train and applies the brakes. Both trains have equal, constant decelerations of 0.9 m/s2. Will there be a collision? (If not how close do they get to one another?) 7. A stone is dropped into the water from a bridge 44 m above the water. Another stone is thrown vertically downward 1.0 s after the first was dropped. Both stones strike the water at the same time. What was the initial velocity of the second stone? 8. A parachutist jumps from a height of 3.1x103 m and falls freely for 10 s. She then opens her parachute, and for the next 20 s slows down with an acceleration of –4.5 m/s2. She then falls the rest of the distance to the ground at a uniform velocity. a) What is her velocity just before the parachute opens? b) At what altitude does the parachute open? c) What is the velocity of the parachutist, just before she strikes the ground? d) Calculate the time required for the whole descent. e) From what height would she have to fall freely in order to strike the ground with the same velocity as she does when wearing a parachute? 9. An efficient parcel service wants to speed up its deliveries by dropping parcels into moving trucks. An employee is positioned on an overpass directly above a straight, level road to drop the parcels into the trucks at just the right time. One day, a delivery truck starts from rest and drives along the road with constant acceleration ½ g. A package is released at the correct instant to land in the truck. If the overpass was 30 m above the truck and the truck started from a position 100 m from the point of impact, how long after the truck started did the employee wait before dropping the parcel? 10. An arrow is aimed and fired at 8.0 m/s horizontally directly at the bulls-eye of a target 22 m away. a) How far below the centre of the bulls-eye will the arrow hit? b) If the target becomes unfastened at the very instant the arrow leaves the bow and falls straight down, where will the arrow strike the target? Explain. c) Would this same thing happen if, instead, a bullet were fired? a tennis ball? 11. Ignoring the curvature of the Earth and air resistance, how far would the following objects each fired horizontally from a height of 2.0 m above the ground travel before hitting the ground: a) a baseball thrown by a throwing machine at 5.0 m/s? b) a baseball thrown by a throwing machine at 20. m/s? c) a bullet fired from a gun at 300. m/s? 12. How far would the same bullet travel on the Moon (assuming it is a perfect glassy sphere as Aristotle claimed)? The acceleration due to gravity on the moon is 1/6 of what it is on Earth.
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