Question

1. A particle moves in one dimension, and its position vs. time is described by the function x0) e (t in seconds, x in meters) (a) At what time(s) is its velocity zero? At what time(s) is its acceleration zero? (b) Make a computer plot(Excel, Matlab or whatever you wish) of x vs. t from 1-o to 5 s. (c) What do you expect to see on the x vs. t graph at the time(s) that v-o? What do you expect to see on the x vs. graph at the time(s) that a 0? Show that the plot you made in (b) agrees with these expectations for the times you found in (a). A passenger train moving at speed vi encounters a freight train a distance d ahead on the same track, moving in the same direction but with a slower speed v2. The brakes are applied on the passenger train, giving it a constant deceleration of magnitude a. (a) Plot a qualitative graph of x vs. for each train. (b) Show that if d < (vi-v2)/(2a), there will be a collision. Interpret this result using the graph of part (a). 2. 3. A rifle with a muzzle velocity of 1200 m/s shoots at a target 230 m away. (a) If the rifle is held perfectly horizontally, at what distance above the target must the rifle be fired so that the bullet hits the target? (b) If on the other hand the bullet exit point is at the same height as the rget, at what angle must the rifle be pointed so that the bullet hits the target? 7 Targer e? Cb)