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Derivatives and Rates of Change- HW problems
1. A particle is moving in a line and its position is given by
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𝑠(𝑡) = 𝑡 3 − 3𝑡 2 + 8𝑡 for 𝑡 ≥ 0.
3
𝑎. Find the velocity and acceleration functions.
𝑏. What is its acceleration at 𝑡 = 4?
𝑐. When is the particle at rest?
𝑑. When is the particle moving in the positive direction? What about
the negative direction?
𝑒. Find the total distance travelled by the particle in the first 6
seconds.
2. A ball is thrown up in the air at 96 ft/sec from the edge of the top
of a building 112 ft above the ground. The position of the ball above
the ground (in feet) at 𝑡 𝑠𝑒𝑐 is given by: 𝑠(𝑡) = −16𝑡 2 + 96𝑡 + 112.
𝑎. Determine the velocity of the ball at time 𝑡.
𝑏. When does the ball reach its highest point?
𝑐. What is the ball’s highest point above the ground?
𝑑. When does the ball hit the ground?
𝑒. With what velocity does the ball hit the ground?
𝑓. What is the acceleration when the ball hits the ground?
𝑔. How far has the ball travelled when it hit the ground?
Derivatives and Rates of Change- HW problems
1. A particle is moving in a line and its position is given by
1
𝑠(𝑡) = 𝑡 3 − 3𝑡 2 + 8𝑡 for 𝑡 ≥ 0.
3
𝑎. Find the velocity and acceleration functions.
𝑏. What is its acceleration at 𝑡 = 4?
𝑐. When is the particle at rest?
𝑑. When is the particle moving in the positive direction? What about
the negative direction?
𝑒. Find the total distance travelled by the particle in the first 6
seconds.
2. A ball is thrown up in the air at 96 ft/sec from the edge of the top
of a building 112 ft above the ground. The position of the ball above
the ground (in feet) at 𝑡 𝑠𝑒𝑐 is given by: 𝑠(𝑡) = −16𝑡 2 + 96𝑡 + 112.
𝑎. Determine the velocity of the ball at time 𝑡.
𝑏. When does the ball reach its highest point?
𝑐. What is the ball’s highest point above the ground?
𝑑. When does the ball hit the ground?
𝑒. With what velocity does the ball hit the ground?
𝑓. What is the acceleration when the ball hits the ground?
𝑔. How far has the ball travelled when it hit the ground?
