Halliday, Resnick & Walker — Motion Along a Straight Line: Problem 39

Cars A and B move in the same direction in adjacent lanes. The position \( x \) of car A is given in Fig. 2.15, from time \( t = 0 \) to \( t = 7.0 \text{ s} \). The figure's vertical scaling is set by \( x_s = 32.0 \text{ m} \). At \( t = 0 \), car B is at \( x = 0 \), with a velocity of \( 12 \text{ m/s} \) and a negative constant acceleration \( a_B \). (a) What must \( a_B \) be such that the cars are (momentarily) side by side (momentarily at the same value of \( x \)) at \( t = 4.0 \text{ s} \)? (b) For that value of \( a_B \), how many times are the cars side by side? (c) Sketch the position \( x \) of car B versus time \( t \) on Fig. 2.15. How many times will the cars be side by side if the magnitude of acceleration \( a_B \) is (d) more than and (e) less than the answer to part (a)?