Assume that you're an insect, and you're flying straight along a line with v= -3t2+12 m/s.  After 1 second of flight, the insect has located 10 meters to the left of its original location. Calculate its displacement from t = 0 to t = 10 secs.

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The bacterium Escherichia coli (or E. coli) is a single-celled organism that lives in the gut of healthy humans and animals. When grown in a uniform medium rich in salts and amino acids, these bacteria swim along zig-zag paths at a constant speed of 20 μm/s. Figure shows the trajectory of an E. coli as it moves from point A to point E. Each segment of the motion can be identified by two letters, such as segment BC. a. For each of the four segments in the bacterium’s trajectory, calculate the x- and y-components of its displacement and of its velocity.b. Calculate both the total distance traveled and the magnitude of the net displacement for the entire motion.c. What are the magnitude and the direction of the bacterium’s average velocity for the entire trip?

Taking north to be the positive y direction and east to be the positive x direction, a particle's position is given byr(t) = (20.2m/s)t^i+(5.15 m/s2)t2^jAt what time, in seconds, is the particle traveling exactly northeast?