Sp 14 Math 170, section 003, Spring 2014 Instructor: Shari Dorsey Current Score : / 26 Due : Wednesday, February :00 AM MST

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1 WebAssign Shari Dorsey Lesson 4-3 Applications (Homework) Sp 14 Math 170, section 003, Spring 2014 Instructor: Shari Dorsey Current Score : / 26 Due : Wednesday, February :00 AM MST 1. /2 points h(t) = 3 + v 0 t 4.9t 2 where h is in meters and t is in seconds. The symbol v 0 is an unknown constant. The velocity of the object is 0 at the instant when t = 2 seconds. Compute v 0. Your answer should be accurate to 1 decimal place. If you are not sure how to determine the units, click here. 2. /2 points h(t) = 12 + v 0 t 4.9t 2 where h is in meters and t is in seconds. The graph of h is shown below. The vertical axis is deliberately without scale. Compute v 0, accurate to 1 decimal place. When does the object hit the ground? Be accurate to 2 decimal places.

2 3. /2 points h(t) = h t 4.9t 2 where h is in meters and t is in seconds. The symbol h 0 is an unknown constant. The object hits the ground when t = 5 seconds. Compute h 0. Your answer should be accurate to 1 decimal place. If you are not sure how to determine the units, click here. 4. /2 points h(t) = 33 + v 0 t 4.9t 2 where h is in meters and t is in seconds. The graph of h is shown below. The vertical axis is deliberately without scale, but the t-axis is positioned exactly at height 0. Compute v 0, accurate to 1 decimal place. When does the object reach its highest point? Be accurate to 2 decimal places.

3 5. /2 points An object is launched straight upward from a platform 10 feet above ground. Its height above ground as a function of time is 1 h(t) = t + at 2 2 where h is in feet and t is in seconds. The symbol a is an unknown constant. Suppose you know that h'(1.25) = 9.75 ft/s. Find a, accurate to 1 decimal place. a = 6. /2 points An object is launched straight upward from a platform. Its height is h(t) = h 0 + v 0 t 16.1t 2 where h is in feet and t is in seconds. Both h 0 and v 0 are unknown constants. At the instant t = 1.5 seconds you know that the height is 50 feet and the velocity is 0. Find both unknown constants, accurate to 1 decimal place.

4 7. /2 points h(t) = h 0 + v 0 t 16.1t 2 where h is in feet and t is in seconds. The graph of h is shown below. The vertical axis is deliberately without scale. Find both unknown constants, accurate to 1 decimal place. 8. /2 points The pressure in a cylinder is given by P(t) = k t where P is in kilopascals (WebAssign abbreviation kpa) and t is in minutes. Assume that t 1 and k is constant. At time t = 7.5 minutes the pressure is changing at 1.35 kpa/min. Find k. k = Your answer should be accurate to 1 decimal place and must include units. If you are not sure how to enter unusual combinations of units, click here.

5 9. /2 points The electrical potential in a circuit is given by V(t) = V 0 (1 e 0.2t ) where V is in volts, t is in seconds, and V 0 is constant. Potential is changing at 2.75 volts/sec at the instant t = 1 second. Find V 0, accurate to 1 decimal place. If you use this method to think about units, you may find it useful to know the following FACT: The output of an exponential function must be dimensionless. I.e., it has no units. V 0 = 10. /2 points The electrical potential in a circuit is given by V(t) = 15 15e kt where V is in volts, t is in seconds, and k is constant. When t = 0 the rate of change of potential is 6.9 volts/sec. Find the rate of change 3 seconds later, accurate to 2 decimal places. Find k, accurate to 2 decimal places, with correct units. You may find it useful to know... FACT: The input to an exponential function must be dimensionless. I.e., it has no units. k = 11. /2 points An object is launched straight upward from a platform above ground. Its height is h(t) = 10 + v 0 t 4.9t 2 where h is in meters and t is in seconds. It hits the ground with a velocity of 25.0 m/s. Find v 0, accurate to 1 decimal place. When did it hit the ground? Be accurate to 2 decimal places.

6 12. /2 points h(t) = h 0 + v 0 t 16.1t 2 where h is in feet and t is in seconds. The graph of h is shown below. Find both unknown constants, accurate to 1 decimal place. 13. /2 points The pressure in a cylinder is given by P(t) = k t where P is in kilopascals (WebAssign abbreviation kpa) and t is in minutes. Assume that t 1 and k is constant. At the instant when pressure is 114 kpa, it is changing at 0.85 kpa/min. When does this happen? Be accurate to 1 decimal place. What is the pressure when t = 1 minute? Round to the nearest kilopascal.