Constant Acceleration Kinematics – Linear and Projectile Motion

Displacement

  1. A rock is thrown straight upward off the edge of a balcony that is 5 m above the ground. The rock rises 10 m, then falls all the way down to the ground below the balcony. What is the rock's displacement?
  1. A child walks 5 m east, then 3 m north, then 1 m east. What is the magnitude of the child's displacement?
  1. An athlete runs exactly once around a circular track with a total length of 500 m. Find the runner's displacement for the race.

Speed and Velocity

  1. If the child from problem 2 completes his journey in 20 seconds, what is the magnitude of his average velocity?
  1. If the runner from problem 3 runs the lap in 1 minute 18 seconds, find his/her average speed and the magnitude of his/her average velocity.
  1. a.) Is it possible to move with constant speed but not constant velocity?
    b.) Is it possible to move with constant velocity but not constant speed?

Acceleration

  1. A car drives in a straight line at a constant speed of 60 miles per hour for 5 seconds. Find its acceleration.
  1. A remote control car is driven along a straight track at 2 m/s. The child controlling the car then activates the toy's turbo mode so that, 3 seconds later, the car's speed is 3.2 m/s. Find its average acceleration.
  1. Shortly after, the remote control car in the previous example exits turbo mode, slowing from 3.2 m/s back to 2 m/s in 2 seconds. Find the car's average acceleration over this interval.

Uniform Acceleration with Equations of Motion

  1. A particle moves along the x-axis with an initial velocity of 4 m/s and constant acceleration. After 3 seconds, its velocity is 14 m/s. How far did it travel during this interval
  1. A car is initially moving at 10 m/s and accelerates at a constant rate of 2 m/s2for 4 seconds, in a straight line. How far did the car travel during this time?
  1. A rock is dropped from a cliff that is 80 m above the ground. If the rock hits the ground with a velocity of 40 m/s, what acceleration did it undergo?

Free Fall

  1. A rock is dropped 80 meters from a cliff. How long does it take to reach the ground?
  1. A ball is thrown straight up with an initial speed of 20 m/s. How high will the ball travel?
  1. One second after being thrown straight down, a rock is falling at 20 m/s. How fast will it be falling 2 seconds later?
  1. An object is thrown straight upward with an initial speed of 8 m/s and strikes the ground 3 seconds later. What height was the object thrown from?

Projectile Motion

  1. A tennis ball is thrown horizontally with an initial speed of 10 m/s. If it hits the ground after 4 seconds, how far did it drop before hitting the ground?
  1. A ball is thrown horizontally from a height of 100 m with an initial speed of 15 m/s. How far does it travel horizontally in the first 2 seconds?
  1. A javelin travels in a parabolic arc for 6 seconds before hitting the ground. Compare its horizontal velocity 1 second after being thrown to its horizontal velocity 4 seconds after being thrown.
  1. A circus performer is launched out of a cannon with a launch angle of 30oand an initial velocity of 40 m/s. How long after launch will it take for the performer to reach the top of his trajectory, and how high is this point?
  1. A cannonball is fired from the ground at a 30oangle with an initial speed of 60 m/s. If the cannonball lands back at the same height it was launched from:
    a.) For how long will the cannonball be in the air?
    b.) How far will it travel horizontally?

Kinematics w/ Graphs

  1. An object's position during a 10 second time interval is shown by the graph below:

    a.) Determine the object's total distance traveled and displacement.
    b.) What is the object's velocity at the following times:t= 1,t= 3, andt= 6.
    c.) Determine the object's average velocity and average speed fromt= 0 tot= 10.
    d.) What is the object's acceleration att= 5?
  2. An object's velocity during a 10 second time interval is shown by the graph below:

    a.) Determine the object's total distance traveled and displacement.
    b.) Att= 0, the object's position isx= 2 m. Find the object's position att= 2,t= 4,t= 7, andt= 10.
    c.) What is the object's acceleration at the following times:t= 1,t= 3, andt= 6.
    d.) Sketch the corresponding acceleration vs. time graph fromt= 0 tot= 10.
  1. An object's position during a given time interval is shown by the graph below:

    a.) At which of the marked points is the object's velocity the greatest? The least?
    b.) Is the object's acceleration positive or negative between points A and B?