A speed skater increases his speed from 10m/s to 12.5m/s over a period of 3s while coming out of a curve of 20m radius. What is the magnitude of the resultant acceleration as he leaves the curve?

During your summer internship for an aerospace company, you are asked to design a small research rocket. The rocket is to be launched from rest from the earth's surface and is to reach a maximum height of 980 m above the earth's surface. The rocket's engines give the rocket an upward acceleration so it moves with the acceleration of 16.0 m/s2 during the time T, that they fire. After the engines shut off, the rocket is in free fall. Ignore air resistance.   What must be the value of T in order for the rocket to reach the required altitude?

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?

A baseball player hits a homerun during a game. The ball leaves his bat at 27 degrees with a speed of 17 m/s. The ball soars into the upper deck 200 m from home plate. The ball takes 3.5 s to reach the upper deck. How high above the ground did the ball land?