Kinematics in One Dimension

For the most part, these problems can be solved using the equations on page one of the EQUATIONS apge. 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 are in place: 1) there is more than one object moving--use a separate table for each (see #below); 2) the object in motion has more than one acceleration during the event--use a separate table for each acceleration (see problem 7); 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 (see #9 below). Have fun. to the odd-numbered appear at the bottom of this page.

.Before proceeding, check the problem solving strategy posted above.

1. A car starts from rest and accelerates at 4 m/s/s for 5.5 s. At that time a) how far has it traveled? b) how fast is it moving.
solution

2. A car moving at 24 m/s slows to 6 m/s while traveling 142 m. a) What acceleration does it experience? b) How long does it take to slow down in this way?

3. A new brand of sports car is advertised to accelerate from zero to 100 km/hr in 7.2 s. a) What is its acceleration in m/s/s? b) How far does the car travel during that time?solution

4. Two drag racers are poised at the starting line, ready to run a 400 m race. Both cars will start from rest at precisely the same instant. Car A has an acceleration of 30 m/s^2; car B is slightly better at 31m/s^2. a) How fast is each car moving as it crosses the finish line? b) By how much time does B finish before A? c) Where is A when B crosses the line?

5. Excessive speed can be a contributing factor in causing accidents because it can foreclose the amount of time and distance available to stop. A driver moving at 60 mi/hr (use its equivalent: 27 m/s) comes over a rise and sees a car stalled in her lane 40 m ahead. She uses .4 sec reaction time before she engages the brakes which give the car an acceleration of -10 m/s^2. Is there a collision? (Hint: What happens to the car during the .4 seconds that the driver needs to engage the brake? solution

6. A car at rest at a stop light accelerates at 4 m/s/s when the light changes. At the same instant that the light changes, a truck overtakes and passes the car traveling at a constant speed of 30 m/s. a) How far from the stoplight is each vehicle when they are traveling at the same velocity? b) How much time has elapsed from the start to this point? At some point in time the car will catch the truck. c) When will that be? d) Where will that be? [Hint: try using equation 3 on page 1 of the equations for the car and the truck. You will get two equations in two unknowns] e) How fast is each moving at the rendez-vous?

7. A subway train starts from rest and accelerates at 3 m/s/s for ten seconds, cruises at a constant speed for thirty seconds, then applies the brakes stopping in 5 seconds. a) What was the speed of the train at the end of the first part of the trip? How does this speed relate to the second and third parts of the trip? b) What acceleration does the train experience during the second and third parts of the trip? c) What is the total distance traveled by the train?solution

8. 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?

9. A car starts from rest and is seen to accelerate at some uniform rate. At check point #1 in the trip the car is traveling at 8 m/s. Seventy meters further down the road the car is moving at 22 m/s. a) How far is check point #1 from the start? b) What time elapsed from the start to check point #1? solution

10) A reasonable estimate of a stopping acceleration is 32 ft//s/s. calculate a stopping distance for each of these speeds: 20 mi/hr, 40 mi/hr, 50 mi/hr. What can one conclude about the need for speed limits?

11/ Southbound on Interstate 95, one can join the Maine Turnpike, a toll road, in Augusta at mile marker # 103. a)How long should it take to travel the full length of that road at the legal limit? 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?

 1. a) x = 60.5 m 1. b) v = 22 m/s 3. a) a = 3.85 m/s/s 3. b) x = 99.7 m 5.  reaction dist = 10.8 m, leaving 29.2 m car needs 36.45 m to stop; accident 7. a) v = 15 m/s; maintains this speed in middle 7 b) a mid = 0; a slow = -6 m/s/s 7. c) x total = 675 m