Police Car Assignment | Professional Writing Services

#4. [Motion Graphs for a Truck & Police Car] A police car is traveling in a straight line (the +x direction) with constant speed vp when a truck traveling at speedup passes the car at time t=0 while going in the same direction. The truck driver realizes she is speeding and immediately begins to slow down at a constant rate until the police car (still traveling at constant speed VP) passes the truck at time tf.

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This happens to be the truck driver’s lucky day, and she isn’t stopped for speeding. (a) On the same set of axes, draw graphs showing velocity vy(t) vs. time t for the police car and truck. Please label any special velocities on the Vx-axis and the time tf on the t-axis. (b) On another set of axes, draw graphs showing position X(t) vs. time t for the car and truck. Please align this set of axes directly under the axes for part (a), and synchronize their t-scales. (c) On each graph, mark and label the times when each vehicle passes the other. (d) On each graph, mark and label the time when the truck is farthest ahead of the police car. Please explain briefly how you identified this time. (e) Using your velocity graphs alone, find the truck’s speed when the police car passes the truck, and show that this speed is independent of the time tf. Please be sure your reasoning is clear. (f) What are the magnitude and direction of the truck’s acceleration while slowing down in terms of Vp and tf)? (g) How far do the two vehicles travel between time t = 0 and t = tf(in terms of Vp and tf)?

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