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Calculus Problems and Tasks - Math Problem Example

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This work called "Calculus Problems and Tasks" describes various tasks, concerning graphics, statistics. The author takes into account descriptive solutions to every calculus problem, necessary explanation, and the result. …
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Calculus Problems and Tasks
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Download file to see previous pages 2. Denote by the position function of an object moving along a straight line, then consider the following definitions: The velocity of the object at time t, denoted by, which is the instantaneous rate of change of h with respect to time, i.e. ;
The speed of the object at time t, denoted by, which is the absolute value of the velocity, i.e. ;
The acceleration of the object at time t, denoted by , which is the instantaneous rate of change of the velocity function with respect to time, i.e.
Adrian received a model rocket for his birthday. The launcher is powered by an air pump, and the height attained by the rocket depends on the number of times Adrian pumps air.  Adrian knows that five pumps will project the rocket upward according to the formula, where is the rocket’s height, measured in feet from the ground, t seconds after take-off.
3. Compute the rocket’s velocity at 2, 3, and 5 seconds.  How do you interpret the difference in signs of the values you obtained?
Solution: The rocket’s velocity at 2 seconds is: -32 (2) + 128 = -64 + 128 = 64 feet/sec. The rocket’s velocity at 3 seconds is: -32 (3) + 128 = -96 + 128 = 32 feet/sec. The rocket’s velocity at 5 seconds is: -32 (5) + 128 = -160 + 128 = -32 feet/sec.
At 2 seconds the velocity is 64 feet/sec and the direction of movement is upward. At 3 seconds the velocity is 32 feet/sec and the direction of movement is upward. At 5 seconds the velocity is -32 feet/sec and the direction of movement is downward. ...Download file to see next pagesRead More
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