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A Problem for MATLAB's Symbolic Computation

Module by: Darryl Morrell. E-mail the author

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Summary: This module contains a problem that can be solved using MATLAB's symbolic computation capabilities.

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Exercise 1

Consider the following problem. Vehicle 1 and Vehicle 2 each move in a straight line. At time t=0 t 0 , Vehicle 1 starts from position 0 with initial velocity 0 and constant acceleration aa. At the same time, Vehicle 2 starts from position s 0 s 0 and travels with constant velocity vv. The position of Vehicle 1 is given by the equation

s=12at2 s 1 2 a t 2 (1)
The position of Vehicle 2 is given by the equation
s=vt+ s 0 s v t s 0 (2)

For given values of a a, v v, and s 0 s 0 , at what time t t will Vehicle 1 to overtake Vehicle 2? At what position will this happen? Plot your solution for t t as a function of a a with v=80 ft/s v 80 ft/s and s 0 =4000 ft s 0 4000 ft .

For given values of v v and s 0 s 0 , what value of a a would cause Vehicle 1 to overtake Vehicle 2 at a given time t t? Plot your solution for a a as a function of t t with v=80 ft/s v 80 ft/s and s 0 =4000 ft s 0 4000 ft .

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