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Free Response Questions


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  • 1. Particle Movement
    10 Free Response
  • 2. Free Response
    (1) A particlemoves alonga straight line with velocity function v(t)= sint-cost andits initial displacement is s(0)= 0 m. Find its position function s(t).
  • 3. Free Response
    (2) A particle moveswith acceleration function a(t)=5t+4t-2t². Its initia; velocity is v(0)= 3m/s and its initial displacement is s(0)= 10m. Find its position after t seconds.
  • 4. Free Response
    (3) A stone is dropped from the upper observation deck (the space deck) of the CN Tower, 450m above the ground.
    a. Find the distance of the stone above ground level at time t.
    b. How long does it take the stone to reach the ground?
    c. With what velocity does it strike the ground?
  • 5. Free Response
    (4) A stone is dropped offa cliff and hit the ground with a speed of 120 ft/s. What is the height of the cliff?
  • 6. Free Response
    (5) If a ballis thrown into the air with a velocity of 40 ft/sec, its height (in feet) after t seconds is given by y= 40t-16t². Find the velcoity when t= 2.
  • 7. Free Response
    (6) If an arrow is shot upward on the moon with a velocity of 58 m/s, its height (in meters) after t secondsis given by h= 58t-0.83t².
    a. Find the velocity of the arrow after one second.
    b. Find the velocity of the arrow when t= a
    c. When will the arrow hit the moon?
  • 8. Free Response
    (7) A particle moves along a straight line and has a position at time t given by x(t)= ln(1+2t²) where x is measured in meters andt in seconds.
    a. find the velocity function, v(t), of the particle.
    b. show that the maximum velocity of the particle is the square root of 2.
  • 9. Free Response
    (8) The displacement s meters of a car, t seconsd after leaving a fixed point A, is given by S= 10t-0.5t².
    a. calculate the velocity when t=0
    b. calculate the value of t when the velocity is zero.
    c. calculate the displacement of the car from A when the velocity is zero.
  • 10. Free Response
    (9) If theacceeration of a particle is given by a(t)= -32 ft/sec² and the velocity of the particle is 64 ft/sec and the height of the particle is 32 ft at time t=0, find
    a. the equation of the particle’s velocity at time t.
    b. the equation for the particles height
    c. the maximum height og the particle
  • 11. Free Response
    (10) A rockis thrown upward with an initial velocity, v(t),of 18 m/s from a height h(t) of 45m. If the acceleration of the rock is at a constant -9 m/s², find the height of the rock a time t=4.
  • 12. Answers Worked Out
    Links to find all ten answers