For the most part, these problems can be solved using the equations on page one of the EQUATIONS page. The trick is to select the right equation; they are not one-size-fits-all. Each equation has four quantities in it, which means you will need to know three quantities to use any equation. It is recommended that, as you read through a problem, you should write down the given information in a table of data. In doing this you must keep like data together. You should keep a separate table of data if any of these conditions is in place: 1) there is more than one object moving--use a separate table for each; 2) the object in motion has more than one acceleration during the event--use a separate table for each acceleration; 3) an ample description of one part of a trip is given, but questions are asked about another part--use a separate table of data for each part. Have fun. 1. A car starts from rest and accelerates and 4 m/s/s. A) How long will take the car to reach a speed of 30 m/s? He) How far will the car travel to get to this point? solution 2. A car is moving to the right at 10 m/s. During the next several seconds, the car is given a push to the left causing its speed to be diminished by 3 m/s during each of those seconds. A) During the time the car is pushed, what acceleration is experience? B) how fast is it going at the end of the each of the first five seconds that the force is applied? C) What can we conclude about negative acceleration always meaning that something slows down? 3. A car is stopped at a traffic light when the light turns green. Now the car accelerates uniformly at a rate of 2 m/s/s. Just as the light turns green, the car is passed by a truck with a constant speed of 20 m/s. A) How far does the car travel before catching the truck? B) How long does this event take? C) At the meeting place, how fast is each vehicle traveling? D) Sketch position-, velocity-, and acceleration vs. time graphs for the situation.solution 4. Car A starts from rest and accelerates and 2 m/s/s. At the same time, but at some distance behind the first car, a second car B also starts from rest and accelerates at 3 m/s/s. The second car overtakes the first after each vehicle has traveled 15 seconds. A) How fast is each car traveling when the second car catches the first? B) How far behind the first car was a second car when race began? C.) sketch position-, velocity-, and acceleration vs. time graphs for the situation. 5. A subway train starts from rest and accelerates at 4 m/s/s for 10 seconds. Now the train travels at a constant speed for 30 seconds. Finally, the train slows uniformly to a halt in five seconds. A) find total distance traveled by the subway train. B) sketch position-, velocity-, and acceleration vs. time graphs for the situation. solution 6. On campus at the University of Some Place, a student is trying to catch a bus. She runs a constant speed of 6 m/s, she can run no faster. At the moment that she is 25 m from the bus, the bus starts from rest and accelerates at 1 m/s/s. A) Does she catch the bus? Hint: determine either the distance traveled by the bus before she catches it or the distance of closest approach is she is not successful. B.) sketch position-, velocity-, and acceleration vs. time graphs for the situation in which she does catch the bus. 7.We will see later in the course that motion on a friction-free inclined plane occurs with uniform acceleration directed down the plane. Block 1 starts from rest and slides down such a plane 20 m long, making the trip in 4 sec. a) What acceleration does the block experience? b) How fast is it moving when it reaches bottom? At he same time Block 1 is released, Block 2 is launched from the bottom.Block 2 travels part way up, stops, and returns to bottom, arriving at the same time as block 1. c) find the launch speed for block 2. d) How far up the plane does it go?solution 8. Two guys decide to impersonate the village idiot and agree to a game of chicken. They speed toward each other, get scared, apply the brakes, but crash anyway. Sketch position-, velocity-, and acceleration as. time graphs for the situation. 9. Waterville is situated at mile marker 127 of Interstate 95 where the posted speed limit is 65 mi/hr. a) How long can a law abiding citizen expect a trip to take to the beginning of the measured roadway? Express your answer in minutes. b) Urban legend has it that the Maine State Police will tolerate an additional 5 mi/hr over the posted limit . How much time does this extra speed save? c) You are likely to be summonsed to court for 75 mi/hr. How much time (vs the first trip) is cut from the trip?. 10. Southbound on Maine Interstate 95, one can join the Maine Turnpike, a toll road, in Augusta at mile marker # 103. The maximum speed allowed on this road is 65 mi/hr. a)What minimum time should it take to travel the full length of that road legally? b) At one time it was suggested that the driver be given a time-stamped card which he/she would surrender upon leaving the turnpike. What would have been the average speed of this vehicle if it arrives at mile zero 15 min early?c) A way to elude detection in this system is to pull over and add minutes to the elapsed time (which also defeats the reason for speeding). Say that a driver travels from marker 103 to Kennebunk marker 24 in 60 minutes. She plans to travel to mile zero at 65 mi/hr. How much time must she spend at roadside to avoid a ticket? 11. The tortoise and the hare agree to a race over a distance of 100 m. The tortoise is to get a running start of .8 m/s, a speed he can maintain indefinitely. The hare's strategy is to wait at the start line until the tortoise is half way to the finish. The hare then will accelerate at .2 m/s/s until his speed is 1.6 m/s and will maintain that speed to the end. a) Who wins the race? b) What is the margin of victory in distance? In time? C.) sketch position-, velocity-, and acceleration vs. time graphs for the situation. This page was last reviewed 01/23/09 |