Question

 A car moves along an r axis through a distance of 900 m, starting at rest (at r = 0) and

ending at rest (at r=900 m). Through the first ¼ of that distance, its acceleration is +2.25 m/s2. Through

the rest of that distance, its acceleration is -0.750 m/s2. What are:

its travel time through the 900 m and

its maximum speed?

Graph position r versus time 1 for the trip,

Graph velocity y versus time 1 for the trip, and

Graph acceleration a versus time 1 for the trip.

Answer 1

Travel time:

$$t_1=\sqrt{2(r/4)/a_1}=14.14\text{ s},\\ t_2=\sqrt{2(3r/4)/a_2}=42\text{ s},\\ t=t_1+t_2=56.14\text{ s}.$$

Max. speed:

$$v=a_1t_1=31.82\text{ m/s}.$$