Walker, Halliday & Resnick — Motion Along a Straight Line: Problem 36

36 A car moves along an x axis through a distance of 900 m, starting at rest (at \( x = 0 \)) and ending at rest (at \( x = 900 \text{ m} \)). Through the first \(\frac{1}{4}\) of that distance, its acceleration is \( +2.25 \text{ m/s}^2 \). Through the rest of that distance, its acceleration is \( -0.750 \text{ m/s}^2 \). What are (a) its travel time through the 900 m and (b) its maximum speed? (c) Graph position \( x \), velocity \( v \), and acceleration \( a \) versus time \( t \) for the trip.