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Rectilinear Motion

Author: Elizabeth Dollhopf

Velocity and Acceleration

the equations of position, velocity and acceleration

First Problem Set

For each position function find

(a) the velocity function

(b) the acceleration function

1. $s open parentheses t close parentheses equals t to the power of 4 minus 4 t squared plus 4 comma space space t greater or equal than 0$

2. $s open parentheses t close parentheses equals 9 minus 9 cos open parentheses straight pi over 3 t close parentheses comma space 0 less or equal than t less or equal than 5$

3. $s open parentheses t close parentheses equals fraction numerator t over denominator t squared plus 4 end fraction comma space t greater or equal than 0$

Source: Calculus Early Transcendentals by Howard Anton, Irl Bivens, Stephen Davis

Speeding Up vs. Slowing Down

Averting a common misconception!

Problem set #2

For the 3 problems you did earlier, also answer the following questions for each one:

(d) At what times is the particle stopped?

(e) When is the particle speeding up? When is it slowing down?

(f) What is the speed of the particle when t=1?

Source: Calculus Early Transcendentals by Howard Anton, Irl Bivens, Stephen Davis