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class code: SPS21 teacher: Mr. Elert
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Physics A: Problem Set 6: Equations of motion

recommended reading

High Marks: 1:22–1:32
Barron's Let's Review: 2.6 The equations of uniformly accelerated motion
physics.info: Equations of motion
Wikipedia: Equations of motion
HyperPhysics: Description of motion
Khan Academy: Kinematic formulas and projectile motion
Physics Girl: 1D motion and kinematics
Mr. Machado: 04 Solving word problems in kinematics I, 05 Solving word problems in kinematics II

classwork

  1. The speed limit of a particular section of freeway is 25 m/s. The right travel lane is connected to an exit ramp with a short auxiliary lane. Cars would have a comfortable deceleration of −2.0 m/s2 for 3.0 s in the auxiliary lane if they were driving at the speed limit.
    1. What speed will cars have when they are done decelerating in this way? (This is also the speed limit of the exit ramp.)
    2. What minimum length should the auxiliary lane be to allow for this deceleration?

    Drivers don't always drive at the speed limit, and highway engineers take this into consideration.

    1. Assume a car could decelerate at four times the "comfortable" rate without losing control. At what maximum speed could a car enter an auxiliary lane with the length you calculated in part b. and still exit at the intended speed?
    2. Assume a driver was traveling on the freeway at the speed you calculated in part c. What distance is needed to decelerate this car to the speed limit of the exit ramp at the "comfortable" rate ?

    Freeway exit

  2. A car with an initial velocity of 60 mph needs 144 feet to come to a complete stop. Determine the stopping distance of this same car with an initial velocity of…
    1. 30 mph
    2. 20 mph
    3. 10 mph
    Note: The rate of change of velocity is not affected by inital velocity in this problem. Fast cars and slow cars slow down at the same rate.

homework

  1. On well-engineered highways obstacles like bridges, retaining walls, and guardrails are often protected by large yellow barrels filled with water or sand called impact attenuators. Should a wayward car find itself on on a collision course with a relatively immovable obstacle, an impact attenuator would help reduce the severity of the crash. If one of these barrels provided sufficient protection for an impact at 30 km/h, how many barrels would provide sufficient protection for an impact at…
    1. 60 km/h?
    2. 90 km/h?
    3. 120 km/h?
  2. A typical commercial jet airliner needs to reach a speed of 180 knots before it can take off. (A knot is a nautical mile per hour and is nearly equal to half a meter per second.) If such a plane spends 30 s on the runway estimate…
    1. its acceleration.
    2. the minimum runway length.
  3. At main engine cutoff (MECO), the Space Shuttle is at an altitude of 113 km (70 miles), traveling 7600 m/s (17,000 mph) relative to the Earth. This occurs 7 minutes 40 seconds into the mission. Determine the downrange distance of the shuttle from lift off to MECO.

drill

For each problem below, select the equation (or pair of equations) that could be used to find the solution. You are not required to completely solve these problems — just start them by selecting from the equations of motion discussed in class.

  1. A plane travels a distance of 500 m while being accelerated uniformly from rest at the rate of 5.0 m/s2. What final speed does it attain?
  2. The speed of a car is increased at a constant rate. If the speed is increased by 42 m/s over a 7.0 s period, what is its acceleration?
  3. If a bullet leaves the muzzle of a rifle with a speed of 600 m/s, and the barrel of the rifle is 0.9 m long, at what rate is the bullet accelerated while in the barrel?
  4. A car traveling at a speed of 20 m/s is accelerated uniformly at the rate of 1.6 m/s2 for 6.8 s. What is its final speed?
  5. Starting from rest, a rocket is accelerated at the uniform rate of 18 m/s2 for 5.0 s. What distance does it travel during this time?
  6. Determine the final speed of a proton that has an initial speed of 6,400 m/s and then is decelerated uniformly in an electric field at the rate of −1,600 m/s2 for 1.5 s.
  7. A plane flying at 110 m/s touches down and travels 302 m before coming to rest. At what rate was the plane decelerated?
  8. A car comes to rest after uniform deceleration at the rate of −9.0 m/s2 for 8.0 s. What distance does it travel during this time?
  9. Determine the distance traveled during constant acceleration by a plane that is accelerated from 66 m/s to 88 m/s in 12 s.
  10. How far does a plane fly while being decelerated uniformly from 140 m/s to 70 m/s in 15 s?