A particle moves in the x-y plane according to r(t) = (4 + 3t3) i + (2 + 2t4) j.  Here distances are measured in meters and times in seconds.  At t = 2 seconds, what angle does the velocity of the particple make with the x-axis?

A river flows due east at 1 m/s and is 100 meters wide.  A swimmer is on the south shore and wishes to cross to a point directly opposite on the north shore.  If the swimmer moves at 1.6 m/s relative to the water, how long will it take them to cross the river? 

A crate of mass m is being pushed at constant speed, v, up a friction-less ramp of angle theta while being acted on by, in addition to gravity and the normal force, two externally applied forces; Fh in the horizontal direction, and Fv vertically down. What is the value of Fv?  

A hiker travels 1 mile east, then 1 mile northwest, and finally 2 miles south.  How far away are they from their starting point?

A box of mass 2 kg is placed on the outer rim of a merry-go-round that has a radius of 6 meters. The coefficient of static friction between the box and the merry-go-round is

You balance a 2 kg block on the palm of your hand. You then lower it, very slowly and gently, a distance of 1.0 meters.  What work do you do on the block? (in Joules)

A plot of the velocity vs. time for a particle moving in one dimension is shown below.  The particle starts from rest at t = 0 seconds and accelerates at a constant rate until t = 2 seconds, when the velocity is 5 m/s.  The particle continues at this speed until t = 5 s and then slows at a constant rate until t = 8 s, when its velocity is zero.  What is the average velocity of the particle between 0 and 5 seconds?  

Consider trying to push a 20 kg block up a 370 frictionless incline (slope) with a force of 200 N applied parallel up the incline. What is the magnitude of the block’s acceleration?  

A particle goes in a circle in the x-y plane.  At an instant in time its velocity is  3m/s i + 4m/s j, and its acceleration is 40 m/s2 i – 30 m/s2 j.  What is the radius of the circle?

A man has a mass of 80 kg. He stands on a bathroom scale in an elevator, and the elevator moves up. As it gets close to the top floor, it slows uniformly from 4 m/s to a stop in a time of 2 s. During this time, what does the scale read (in kg)?