Kinematics Problems



Kinematics Problems – Use the GUESS method to solve the problems

** If it starts from rest, vo = 0 m/s. If it ends at rest, vf = 0 m/s. **

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1. A racecar accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. Determine the acceleration of the car.

2. Rocket–powered sleds are used to test the human response to acceleration. If a rocket-powered sled is accelerated from rest to a speed of 444 m/s in 1.8 seconds, then what is the acceleration of the sled travels?

3. The Lamborghini Murcielago can accelerate from 0 to 27.8 m/s in a time of 3.40 seconds. Determine the acceleration of this car.

4. During the annual shuffleboard competition, Renee gives her puck an initial speed of 9.32 m/s. Once leaving her stick, the puck slows down at a rate of -4.06 m/s/s. Determine the time it takes the puck to slow to a stop.

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5. An airplane accelerates from rest down a runway at 3.2 m/s2 for 32.8 seconds until it finally lifts off the ground. Determine the distance traveled before take-off.

6. A car starts from rest and accelerates uniformly for 5.21 seconds over a distance of 1100 m. Determine the acceleration of the car.

7. At the end of a bike race, the second place bicyclist sees the finish line and accelerates at a rate of 0.9 m/s2 to try to catch the winner. If he was initially moving at 8.6 m/s and accelerated for 2.0 seconds, how far did he travel?

8. During the annual shuffleboard competition, Renee gives her puck an initial speed of 9.32 m/s. Once leaving her stick, the puck slows down at a rate of -4.06 m/s/s. After 2.3 seconds, how far had the puck traveled?

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9. A bike accelerates uniformly from rest to a speed of 7.10 m/s over a distance of 35.4 meters. Determine the acceleration of the bike.

10. An engineer is designing the runway for an airport. Of the planes that will use the airport, the lowest acceleration rate is likely to be 3 m/s2. The lowest take-off speed will be 65 m/s. Assuming these minimum parameters, what is the minimum allowed length of the runway?

11. It was once recorded that a Jaguar left skid marks that were 290 meters in length. Assuming that the Jaguar skidded to a stop with a constant acceleration of –3.90 m/s2, determine the speed of the Jaguar before it began to skid.

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12. A racecar accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. Determine the distance traveled.

13. Rocket–powered sleds are used to test the human response to acceleration. If a rocket-powered sled is accelerated from rest to a speed of 444 m/s in 1.8 seconds, then what is the distance that the sled travels?

|Given / Unknown |Equation |Substitute |Solve with units |

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|t = | | | |

|a = | | | |

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Mixed Practice (There might be a constant speed question mixed in . . . .)

Use the GUESS method to solve the problems

1. A car traveling at 22.40 m/s skids to a stop in 2.550 seconds. Determine the skidding distance of the car.

2. A Formula One car is a single-seat racing car with an open cockpit and substantial wings located in the front and rear. At high speeds, the aerodynamics of the car help to create a strong downward force which allows the car to brake from 27.8 m/s to 0 in as small of a distance as 17 meters. Determine the deceleration rate (i.e., acceleration) achieved by such a car.

3. A Cessna 150 airplane has a takeoff speed of 28 m/s (63 mi/hr). Determine the minimum length of the runway which would be required for the plane to take off if it averages an acceleration of 1.9 m/s/s.

4. Homer Agin leads the Varsity team in home runs. In a recent game, Homer hit a 42.9 m/s sinking curve ball head on, sending it off his bat in the exact opposite direction at -25 m/s. The actually contact between ball and bat lasted for 0.75 milliseconds. Determine the magnitude of the average acceleration of the ball during the contact with the bat.

5. In last week's Homecoming victory, Al Konfurance, the star halfback of South's football team, broke a tackle at the line of scrimmage and darted upfield untouched. He averaged 9.8 m/s for an 80-yard (73 m) score. Determine the time for Al to run from the line of scrimmage to the end zone.

6. Rickey Henderson, baseball's record holder for stolen bases, approaches third base. He dives head first, hitting the ground at 6.75 m/s and reaching the base at 5.91 m/s, accelerating at -5.11 m/s/s. Determine the distance Rickey slides across the ground before touching the base.

7. Win Blonehare and Kent Swimtashore are sailboating in Lake Gustastorm. Starting from rest near the shore, they accelerate with a uniform acceleration of 0.29 m/s/s, How far are they from the shore after 18 seconds?

8. *A bullet is moving at a speed of 367 m/s when it embeds into a lump of moist clay. The bullet penetrates for a distance of 0.0621 meters. Determine the acceleration of the bullet while moving into the clay.

9. *In the Funny Car competition at the Joliet Speedway in Joliet, Illinois in October of 2004, John Force complete the ¼-mile dragster race in a record time of 4.437 seconds. Determine the average speed of the dragster in m/s. GIVEN: (1.000 mi =1609 m)

10. *Cynthia competes in luge competitions during the winter months. She rides solo on a small sled 3 inches off the ground down icy slopes, turning only by use of her feet and the shifting of her weight on the sled. During the initial stage of one downhill luge, Cynthia accelerated from rest at 6.84 m/s/s for 2.39 seconds. Determine the distance she moved during this acceleration phase.

11. *Suzie Lavtaski has reached the end of the ski slope and abruptly decelerates from 29.0 m/s to 1.8 m/s in 1.45 seconds. Determine Suzie' acceleration rate and the distance she moved during this braking period.

Kinematic Equations (velocity is changing)

[pic] use when you don’t need x

[pic] use when you don’t need t

[pic] use when you don’t need vf

[pic] use when you don’t need a

Kinematic Variables:

|Variable |Measurement |Unit |

|v | | |

|vo = initial velocity |Speed/Velocity |Meters/Second (m/s) |

|vf = final velocity | | |

|t |Time |Time (s) |

|a |Acceleration |Meters/Seconds2 (m/s2) |

|x |Distance/Displacement |Meters (m) |

Vectors/Scalars:

|Scalar |Example |

|Have magnitude only. |Magnitude means size! How big? |

|Distance |4 m |

| Speed |43 m/s |

|Time |56 s |

|Vector |Example |

|Have magnitude and direction. |Direction is the way a vector points. |

|Displacement |4 m, North |

|Velocity |43 m/s Down |

|Acceleration |2m/s2, Left |

Directions:

|Positive |Negative |

|North, Up |South, Down |

|East, Right |West, Left |

Vector directions:

|Vector |Positive |Negative |

|Displacement |Traveled forwards |Traveled backwards |

|Velocity |Moving forwards |Moving backwards |

|Acceleration |Speeding up |Slowing down |

Answers:

1. 11.2 m/s2

2. 247 m/s2

3. 8.18 m/s2

4. 2.3 s

5. 1721 m

6. 81.0 m/s2

7. 19 m

8. 10.7 m

9. 0.712 m/s2

10. 704 m

11. 47.6 m/s

12. 79.8 m

13. 400 m

Mixed Review:

1. 28.6 m

2. -22.7 m/s2

3. 210 m

4. 90,476 m/s2

5. 7.5 s

6. 1.04 m

7. 47 m

8. -1.08 x 106 m/s2

9. 90.7 m/s

10. 19.5 m

11. A = -18.8 m/s2 and x = 22.3 m

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