BC 1-2
Problem Set #1
Spring 2016
Name
Due Date: Tuesday, January 26 (at beginning of class)
Please show appropriate work – no big calculator leaps – except as indicated. Work should be shown
clearly, using correct mathematical notation. Please show enough work on all problems (unless
specified otherwise) so that others could follow your work and do a similar problem without help.
Collaboration is encouraged, but in the end, the work should be your own.
1.
Sketch a possible graph to represent the following situation. Be sure to indicate and label key
points and intervals of your graphs. You should label both horizontal and vertical scales with
reasonable values.
A man climbs a ladder up to the top of a high dive platform, dives off into the pool, and then
swims over to the side of the pool. Sketch his speed as a function of time.
speed
time
2. Given the graph of a displacement function below, sketch the velocity on the same set of axes.
BC 1-2
Problem Set #1 p.1
Spring 2016
3. Given the graph of a velocity function below, sketch the displacement on the same set of axes.
Assume the displacement at t = 0 is 0.
4. The displacement curve s (t ) and velocity curve v (t ) of a particle satisfy the conditions that s (1)  1
, s is concave down, and (s(t ))2  v(t ) . Describe the path of the particle in as much detail as possible.
BC 1-2
Problem Set #1 p.2
Spring 2016
5) A tall, thin vase with circular cross sections has cross-sectional area as given below, where the x-axis
represents the height of the vase in inches, and the y-axis is the area of the cross-sectional circle in units of in 2 .
Water is poured into the vase at a rate of 1 in 3 /sec. Create a graph of the height of the water in the vase, in
inches, as a function of time, in seconds. Explain any relevant features of the graph. Label the scales on both
axes; while these will not be exact, the numbers should be reasonable.
y





x












.
BC 1-2
Problem Set #1 p.3
Spring 2016