University:
Missouri State University
Course:
MTH 103 | Intermediate Algebra
Academic year:

2022
Views:

330

Pages:

2
Author:

alkilowyx84

Calculus Section 4.1 – Applications (Position, Velocity & Acceleration) Worksheet Name: ___________________________ Date: ________________ Block: ____ Solve each of the following applications. 1. The position equation of the movement of a particle is given by s  (t 2  1)3 where s is measured in feet and t is measured in seconds. Find the acceleration at 2 seconds. 2. Suppose the position equation of a moving object is given by s (t )  3t 2  2t  5 where s is measured in meters and t is measured in seconds. Find the velocity of the object when t = 2. 3. An object is thrown downward from the top of a 220 ft. building with an initial velocity of 26 ft/sec. Write the position equation for the movement described. What is the velocity at 1 second? 4. A particle moves in a straight line according to the law of motion: s  t 3  4t 2  3t . When the velocity of the particle is zero, what is the acceleration? 5. At t = 0, a rock is dropped from rest atop a 256 ft high building. When, and with what velocity does it strike the ground? 6. A rocket is shot vertically from the ground with an initial velocity of 608 ft/sec. When does the rocket reach its maximum height, and what is the maximum height? When does the rocket hit the ground? 7. A stone is thrown straight down from the top of an 80 ft tower. If the initial speed is 64 ft/sec, how long does it take to hit the ground, and with what speed? 8. A rocket is shot vertically from the ground and reaches a height of 256 ft after 2 sec. What was its initial velocity, what will be its maximum height, and when does it reach its maximum height? 9. A car is moving along a straight road according to the equation: s  2t 3  3t 2  12t . Describe its motion by indicating when the car is moving to the right, and when it is moving to the left. 10. A rock is dropped down a well that is 256 ft deep. When will it hit the bottom of the well? 11. A rock is thrown straight down from a height of 480 ft with an initial velocity of 16 ft/sec. How long does it take to hit the ground? With what speed does it hit the ground? How long does it take before the rock is moving at a speed of 112 ft/sec? When has the rock traveled a distance of 60 ft? 12. A rocket is shot straight up from the ground. What must have been its initial velocity if it returned to the earth in 20 seconds? Calculus Section 4.1 – Applications (Position, Velocity & Acceleration) Worksheet Name: ___________________________ Date: ________________ Block: ____ Solutions: 1. a  342 ft 2. v (t )  14 m sec2 s 3. s (t )  16t 2  26t  220 v (t )  58 ft sec downward 4. a  10 5. t  4 sec with a velocity of 128 ft sec downward 6. reaches max height at t  19 sec ; max height is 5776 ft 7. t  1 sec with a speed of 96 m 8. v 0  160 ft sec sec downward ; reaches max height of 400 ft at t  5 sec 9. left: [0,2) & right: (2, ) 10. t  4 sec 11. t  5 sec with a speed of 176 ft 12. v 0  320ft sec sec downward; it takes 3 sec ; traveled 60 ft at t  3 sec 2