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# Free Response Questions

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### Free Response Questions

1. 1. Particle Movement<br />10 Free Response<br />
2. 2. Free Response<br />(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). <br />
3. 3. Free Response<br />(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. <br />
4. 4. Free Response<br />(3) A stone is dropped from the upper observation deck (the space deck) of the CN Tower, 450m above the ground.<br /> a. Find the distance of the stone above ground level at time t.<br />b. How long does it take the stone to reach the ground?<br />c. With what velocity does it strike the ground? <br />
5. 5. Free Response<br />(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?<br />
6. 6. Free Response<br />(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.<br />
7. 7. Free Response<br />(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.<br />a. Find the velocity of the arrow after one second.<br />b. Find the velocity of the arrow when t= a<br />c. When will the arrow hit the moon? <br />
8. 8. Free Response<br />(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.<br />a. find the velocity function, v(t), of the particle.<br />b. show that the maximum velocity of the particle is the square root of 2.<br />
9. 9. Free Response<br />(8) The displacement s meters of a car, t seconsd after leaving a fixed point A, is given by S= 10t-0.5t².<br />a. calculate the velocity when t=0<br />b. calculate the value of t when the velocity is zero.<br />c. calculate the displacement of the car from A when the velocity is zero. <br />
10. 10. Free Response<br />(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<br />a. the equation of the particle’s velocity at time t.<br />b. the equation for the particles height <br />c. the maximum height og the particle<br />
11. 11. Free Response<br />(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.<br />