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Acceleration Problems

 

1.  If you rollerblade at an average speed of 9 miles per hour for 3.5 hours, how far will you travel? Hint:  Use the formula d = rt     (distance = rate * time)

 

 

2.  An amusement park ride averages 30 miles per hour during the 2 1/2 minute ride. How far does the ride travel?  Hint:  Use the formula d = rt (distance = rate * time)Remember to change the time from minutes to hours to match the unit in the rate.

 

 

3.  In a cross-country race, a driver drove her car 805 kilometers (km) in 7 hours.  What was her average speed?  Hint:  Use the formula d = rt (distance = rate * time) Solve the formula for r, then use the given information to find the value of r. 

 

4.  Two friends hike a mountain trail.  Darrel starts out on a trail at a pace of 4 kilometers per hour (k/h).  One hour later, Roberto starts out on the same trail at 6 k/h. How long will it take Roberto to catch up to Darrel?

 

Hint:  This problem involves two objects moving in the same direction at different rates for different times.  Create a model for each hiker.  At the time Roberto catches up to Darrel, they have both traveled the same distance. Use the formula d = rt once for each hiker. Set the two expressions equal. Solve for time. 

 

5.  Sarah begins hiking at a pace of 4 kilometers per hour (k/h) from one end of a trail that is 34 kilometers long. Amanda begins one hour later at the other end of the trail, walking towards Sarah at a pace of 6 k/m.  How long will it take for the two hikers to pass each other?

 

Hint:  This problem involves two objects moving in opposite directions at different rates for different times.  Create a model for each hiker.  When the two hikers pass each other, their total distance hiked is 34 kilometers.  Use the formula d = rt once for each hiker. Sum the two expressions and set equal to 34. Solve for time. 

 

  1. Aaron and Rebecca are entered in the 26-mile marathon race.  Rebecca's average rate is 5 miles per hour (mph) and Aaron's average rate is 8 mph.  Both runners start at the same time.  How far behind will the slower runner be when the faster runner crosses the finish line?  Hint:  This problem involves two objects moving in same direction at different rates for different times.  Create a model for each runner.  When Aaron crosses the finish line, Rebecca distance to go will be 26 miles minus the distance she has run when Aaron finishes.  Use the formula d = rt once for each runner.  Solve for Aaron's time and use that value to solve for Rebecca's distance to go. 

 

7.  A family drives from their home to an amusement park at an average speed of 50 miles per hour (mph).  The return trip is made at an average of 60 mph and the trip home took 15 minutes less time than the trip to the park.  How far away from their home is the amusement park?  Hint:  This problem involves one object moving in two different directions at different rates for different times.  Also, there are two different time units; change all times to hours.  Create a model for part of the round trip.  The distance on each pat must be the same.  Use the formula d = rt once for each part of the round trip. Set the two expressions equal. Solve for time, then use that value to solve for distance. 

 

  1.  A jet traveled from New York to Mexico City at an average speed of 500 knots (1 knot = 1 air mile per hour).  Because of a very strong west-to-east tailwind, the average speed for the return trip was 600 knots.  The return trip from Mexico City took 42 minute less than the trip going there. What is the air distance between New York and Mexico City?  Hint:  This problem involves one object moving in two different directions at different rates for different times.  Also, there are two different time units; change all times to hours.  Create a model for each part of the round trip.  The distance on each part must be the same.  Use the formula d = rt once for each part of the round trip.  Set the two expressions equal.  Solve for time, then use that value to solve for distance. 

 

9.  A machine arm moves in a left-to-right-to-left motion.  It moves twice as fast to the right as it does to the left.  A complete left-to-right-to-left cycle takes 3 seconds to complete.  The rate of travel when moving to the left is 10 centimeters per second (c/s).  How far does the machine arm move in each direction?  Hint:  This problem involves one object moving in two different directions at different rates for different times.  The two rates are given and the two times are related by the time required for a total cycle.  Create a model for each direction of motion.  The distance traveled in each direction must be the same.  Use the formula d = rt once for each direction of the cycle.  Set the two expressions equal.  Solve for time, then use that value to solve for distance.