University Physics SI: 1-16-2014
Objective: Basic Review; Introduction to Critical
Thought
SI Leader: Kevin Tokoph
ktokoph@patriots.uttyler.edu
Dimensional Analysis
1.
Convert 50 km to:
a. Feet:
b.
Inches:
c.
megameters:
d.
nanometers:
2.
Convert the speed of light (c= 2.998 x 10 8 m/s) to feet/year.
3.
Convert π radians/182.5 days to degrees/minute.
a. CONVERSION FACTOR for RADIANS/DEGREES: _____________________________________
BASIC TRIGONOMETRY
4.
Compute the following without a calculator: (DO YOU KNOW THE RIGHT HAND RULE FOR TRIG??!!)
a. Sin (π/2)
b. Cos (π/2)
c. Tan (π/2)
d. Sin (π/3)
e. Cos (π/3)
f. Tan (π/3)
g. Sin (π/4)
h. Cos (π/4)
i. Tan (π/4)
j. Sin (π/6)
k. Cos (π/6)
l. Tan (π/6)
m. Sin (0)
n. Cos (0)
o. Tan (0)
p. 1/sin (x)
q. 1/cos (x)
r. 1/tan (x)
5.
6.
7.
The derivative of a function is ________________________________________________.
The integral of a function is __________________________________________________.
Differentiate the following functions:
a. 4x3 + 3x2 + 7x = f(x)
b. (5x2)(7x) = g(x)
c. (3x2)/ (4x + 8) = h(x)
d. ln (6x) = j(x)
e. exp(9x) = k(x)
f. 3x = m(x)
Integrate the following functions:
a. 4x3 + 3x2 + 7x = f(x)
b. ln (6x) = j(x)
c. exp(9x) = k(x)
d. 3x = m(x)
e. (2ex)(3x) = n(x)
f. (x2 + 9)(1/2) = p(x)
8.
PROBLEMS
9.
Kev starts running from point A in the π/6 direction for 4 minutes. He runs 0.5 miles in that time. Find the following in any
units:
a. The distance in the x-direction:
b. The distance in the y-direction:
c. Average velocity in the x-direction:
d. Average velocity in the y-direction:
10. ATP synthase is an enzyme in the mitochondria of cells. It rotates clockwise to produce the energy of your body! In 1 second,
it rotates approximately 16 radians.
a. How many degrees has it rotated in 1 hour?
b.
If 3 ATP are produced per 2π radians, approximately how many ATP are produced in that 1 hour?
11. Draw the velocity vs time graph for a particle whose movement is mimicked by the graph of sin(x). Assume the y-axis of
sin(x) corresponds to the velocity axis on your graph. Does the particle ever have acceleration?
12. Displacement is the __________________________ of velocity.
13. Acceleration is the __________________________ of velocity.
1. For the position-versus-time graph given below, assume the same scaling of the time axis as above.
c.
d.
e.
a.
Determine the average velocity of the object between t = 0 s and t = 2 s.
(Answer: 1.25 m/s)
b.
Determine the average velocity of the object between t = 2 s and t = 7 s.
(Answer: -0.8 m/s)
At t = 1 s, is it moving leftward, moving rightward, or stopped? Explain your answer.
At t = 5 s, is it moving leftward, moving rightward, or stopped? Explain your answer.
At t = 3 s, is it moving leftward, moving rightward, or stopped? Explain your answer.
2. For the velocity-versus-time graph given below, assume the same scaling of the time axis as above (1 s per tick). The graph
represents the velocity of an object that is located at the position x = -1 m at t = 0 s.
a. What is the position of the object at t = 2 s? (Answer: x = -13 m)
b. What is the position of the object at t = 6 s? (Answer: x = -21 m)
a. What is the total displacement between t = 3 s and t = 8 s? (Answer: Δx = +5 m
NEW MATERIAL
1.
2.
3.
4.
5.
6.
Write the formulae for the following:
a. Average velocity: _______________________________________
b. Instantaneous velocity: ________________________________________
c. Average acceleration: ______________________________________
d. Instantaneous acceleration: ________________________________________
If velocity is constant at 10 m/s, what is the total displacement if a particle takes 4 seconds to get to a final position of 5 m
with respect to the origin (x = 0 m)?
The velocity of a particle is given by v(t) = 2x3 + x2 -5x.
a. Find the acceleration at t = 4 seconds.
b. Find the velocity at t = 2 seconds.
c. Find the position of the particle at t = 3 seconds if the particle begins at x = -20 m with respect to the x-axis.
d. Does the object have a turning point? If so, at what time is the turning point?
e. Explain in (d) how you know where a turning point lies.
f. Does the particle have a change in acceleration? Express the formula if so.
Find the total displacement given the following displacement vector A, B, and C.
a. A = < 2, 5, -4 >
b. B = < 3, -2, 4 >
c. C = < -1, 3, 3 >
Note the following displacement formula for a particle in unit vector notation:
a. S(t) = 5i + 3j – 4k
b. Evaluate the total displacement if each vector is doubled.
c. Evaluate the total displacement if each vector is quadrupled.
d. Evaluate the total displacement if the particle reverses its direction in the x and y directions.
While exploring a cave, a spelunker starts at the entrance and moves the following distances. She moves 50 meters north, 30
meters southwest, 100 meters at an angle 30 degrees North of East. Find the magnitude and direction of the spelunker’s total
displacement.

7.

Given vectors A  4iˆ  3 ˆj and B  6iˆ  2 ˆj
a. Find the magnitude and direction of vector A.
b. Find the magnitude and direction of vector B.
c.
d.



Find the x and y components of vector C where A  B  C
Find the magnitude and direction of the vector C.
0.



e. Find the vector D in both component form and in terms of magnitude and direction where D  2 A  B
8. Derive the following kinematics equations:
a. Position equation:
b. Velocity equation:
c. The position equation out to 6 terms:
d. In (c), what happens to each successive term in terms of its overall contribution to the overall displacement,
generally?
9. Draw the motion diagram for an object that is thrown straight upward and then falls back downward to the ground. Include
velocity and acceleration vectors with respect to time.
a. To what type of problem could this correspond?
10. Draw the motion diagram with velocity and acceleration vectors with respect to time for the following circumstances:
a. A ball rolling up and inclined plane
b. A ball rolling down a declined plane
c. Draw a position vs time graph and a velocity vs. time graph for each of these.
11. If the position function is cubic, _________.
a. The velocity is _______________________.
b. The acceleration is _____________________.
c. The jerk is _________________________.
d. The jounce is _________________________.