Halliday, Resnick & Walker — Motion Along a Straight Line: Problem 15

(a) If a particle’s position is given by \( x = 4 - 12t + 3t^2 \) (where \( t \) is in seconds and \( x \) is in meters), what is its velocity at \( t = 1 \text{ s} \)? (b) Is it moving in the positive or negative direction of \( x \) just then? (c) What is its speed just then? (d) Is the speed increasing or decreasing just then? (Try answering the next two questions without further calculation.) (e) Is there ever an instant when the velocity is zero? If so, give the time \( t \); if not, answer no. (f) Is there a time after \( t = 3 \text{ s} \) when the particle is moving in the negative direction of \( x \)? If so, give the time \( t \); if not, answer no.