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REVIEW GUIDE: MATH BASICS
For the following problems, solve for any unknowns. Show all work and box all answers.
Unclear work will not be graded.
1. Solve for x and/or y.
a) 2x-4 = 2
b) 4y2 + 5 = 10+y
c) 2x – y = 10
x + 3y = -2
d) 2y+x = 0
5x + 3y = -35
2. Convert the following distances into meters.
a) 10cm
c) .9mm
b) 12km
d) 6x103 km
3. Convert the following masses into kilograms.
a) 250g
b) .055g
4. Convert the following times into seconds.
a) 28 days
b) 7.5 hours
b) 45 minutes
d) 2 years
5. Convert the following weights into masses for an object on Earth.
a) 150N
b) .4N
6. Convert the following weights into masses for an object on the Moon where gravity
is 1/6 that of Earth’s.
a) 250N
b) .54N
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7. Solve for the value of A and x for the triangle given to
the right.
8. Solve for the values of X and Y for the triangle given
to the right.
9. Graph the following data tables and
find the equation that best fits the
line. If the line is non-linear, linearize
the line and write that equation. You
may graph both part a and part b on
the same graph. Be sure to label
your axes.
a
b
X
T
X
T
2
0
0
0
6
2
.5
1
10
4
2
2
14
6
4.5 3
18
8
8
4
10. Convert the following numbers into scientific notation.
a) .000045
b) 6371000
11. Convert the following numbers from scientific notation.
a) 5.8x103
b) 3x10-8
10. What units must position be in for a final answer?
11. What units must time be in for a final answer?
12. What units must mass be in for a final answer?
13. What units must weight be in for a final answer?
14. What is the difference between a scalar and vector quantity?
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REVIEW GUIDE: KINEMATICS
For the following problems, solve for any unknowns. Show all work and box all answers.
Unclear work will not be graded. Use g=10m/s2.
1. Fill in the blank for the following statements.
a) The slope of a position versus time graph is
.
b) The slope of a velocity versus time graph is
.
c) The area under an acceleration versus time graph is
.
d) The area under a velocity versus time graph is
.
2. What is the difference between distance and displacement?
3. What is the difference between speed and velocity?
4. What is the difference between average velocity and instantaneous velocity?
5. A car traveling a constant velocity of 20m/s travels for 3 hours. What is the total
distance the car went?
6. A plane traveling East can travel 200 miles in 2 hours and traveling West on the way
back can make the same trip in 1.5 hours.
a) What is the total distance the plane travels in one round trip?
b) What is the total displacement of the plane after one round trip?
c) What is the plane’s average speed?
d) What is the plane’s average velocity?
7. A car accelerates from rest to a top speed of 45m/s. If the car completed this
acceleration in 5 seconds:
a) What is the car’s acceleration?
b) What is the distance the car traveled while accelerating?
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8. A ball is released from rest from a 10m tall building where air resistance is
negligible.
a) What is the time it takes the ball to fall all 10 meters?
b) What is the final velocity of the ball after falling 10 meters?
c) If someone were to instead thrown the ball downward at 10m/s, what would be
the time it takes the ball to fall 10 meters?
9. A cannonball is fired horizontally from the top of a 100m tall cliff at 20m/s.
a) What is the time it takes for the cannonball to fall?
b) What horizontal distance from the base of the cliff will the cannonball land at?
10. What is the best angle from which a projectile will travel the furthest horizontal
distance when fired from level ground?
11. What angle(s) will a projectile travel no horizontal distance?
12. If a ball is fired straight up at a velocity of +10m/s, what will the:
a) Velocity be at the top?
b) Acceleration be at the top?
c) Velocity be once it returns to the person’s hand?
13. If a ball is fired at a 45o angle at 50m/s, what will the:
a) Velocity be at the top?
b) Acceleration be at the top?
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REVIEW GUIDE: FORCES
For the following problems, solve for any unknowns. Show all work and box all answers.
Unclear work will not be graded. Use g=10m/s2. For any force problem, draw the FBD
and write the force equations.
1. What are Newton’s three laws?
2. What are the units for:
a) Force
b) mass
c) Acceleration
d) Coefficient of friction
3. Answer true (T) or false (F) for the following statements.
a) An object is experiencing no forces if it is not moving.
b) An object is experiencing no forces if it is moving at a constant velocity.
c) An object is experiencing a net force if it is accelerating.
d) If you push on a car with 400N of force, the car pushes back more.
e) You exert the same force on the Earth as the Earth does on you.
f) An object in motion will stay in motion regardless of other forces.
4. A person is pushing a 3kg box across the floor at a constant rate. If the person is
applying a 25N horizontal force, what is the coefficient of friction between the box
and the floor?
5. The same person in #4 pulls the box with 60N of force. What is the acceleration of
the box?
6. An elevator is accelerating upward at .1m/s2. If the elevator has a mass of 750kg
and carries 250kg of passengers inside, what is the tension in the rope holding the
elevator up?
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7. A 4kg box sits motionless on a slope that is 30o up from the horizontal. What is the
coefficient of friction between the slope and the box for it to not move?
8. If the box were sitting on a frictionless slope tilted at the same angle, what would its
acceleration be?
9. A grocery bag with 2.5kg of content inside can withstand a net force of 30N before
ripping. If the bag is accelerated upward at 6m/s2, what is:
a) The upward force pulling on the bag? Will the bag withstand this force?
b) The maximum acceleration that the bag could withstand without ripping?
10. What is the range the coefficient of friction can be between?
11. The Earth pulls down on you. What is the reaction pair to this force?
12. You push on a wall. What is the reaction pair to this force?
13. A horse pulls on a cart so that it moves forward at a constant velocity. What is the
reaction pair to this force?
14. An Attwood machine with a cart of mass m1=450g is
accelerated at 1.2m/s2 by a hanging mass. What is the
value of the weight of the hanging mass for the cart to
accelerate at 1.2m/s2?
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REVIEW GUIDE: ENERGY
For the following problems, solve for any unknowns. Show all work and box all answers.
Unclear work will not be graded. Use g=10m/s2. Write the conservation of energy
equations for any mathematical problem.
1. Describe the law of conservation of energy in your own terms.
2. What are the units for:
a) Kinetic Energy
b) Spring Energy
d) Work
e) Power
c) Gravitational Potential Energy
3. A .5kg ball rolling at 4m/s on a flat table 1 meter tall falls to the floor.
a) How much energy did it have before falling?
b) What is its final velocity?
4. A person pushes a 4kg box for 2 seconds from rest. After being pushed, it has a
final velocity of 2m/s.
a) What is the work the person did on the box?
b) What is the power exerted by the person?
5. If the force applied to an object does not displace it, is there any work done?
6. If the force applied to an object is perpendicular to its motion, is there any work
done?
7. A horizontal spring with a constant of 20N/m is compressed so that it fires a .25kg
ball at 10m/s. By how much was the spring compressed?
8. A small kitten jumps down from a wall of height h and lands with a velocity of v.
a) Write the final velocity of the kitten all in terms of numbers and variables.
b) If the wall is 2.2 meters tall, what is the final velocity of the kitten?
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9. A ball is dropped from a height h and hits the floor with a velocity v. If the height is
doubled, what is the new final velocity of the ball in terms of variables?
10. How much work does the Earth do on a 2kg ball that is released from rest from 2
meters above the surface?
11. How much power is exerted by Earth in problem 10?
12. A 1500kg car moving at 40m/s experiences a drag force of 2.4x10 6N. What is the
power exerted by the car as it travels at a constant velocity?
A 65g tennis ball is dropped from rest from a 4m tall landing. If the tennis ball compresses
3cm before it bounced, what is the spring constant of the tennis ball?
A 500N box slides down a frictionless ramp whose hypotenuse is 10 meters long. What is
the final velocity of the box?
How much work is done by a 60kg person riding a 30kg bike while they accelerate at 4m/s2
for 3 seconds?
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REVIEW GUIDE: MOMENTUM
For the following problems, solve for any unknowns. Show all work and box all answers.
Unclear work will not be graded. Use g=10m/s2. Write what the initial momentum and
final momentum are for all word problems.
1. What is the definition of conservation of momentum?
2. What are the units for:
a) Momentum
b) Impulse
3. What is an elastic collision?
4. What is an inelastic collision?
5. What kind of collision causes a loss of kinetic energy?
6. Explain the conditions for when momentum is conserved.
7. A 70g hockey puck is hit by a hockey stick for .1 seconds. If the hockey puck has a
final velocity of 15m/s, what was the force delivered to it?
8. Two ice skaters initially holding hands push off from each other. What is the mass of
one ice skater if they have a final velocity of 4m/s and the other has a mass of 55kg
and travels at 5m/s?
9. A 1000kg car traveling at 15m/s collides with a 2000kg car initially traveling at 5m/s.
What is the final velocity of the two cars once they collide and stick together?
Explain why their final velocity is between the initial velocity of the 1000kg car and
the 2000kg car.
10. A 50kg person stuck in the middle of a frozen pond decides to thrown their 2kg boot
to get themselves back to land. If they throw the boot at 20m/s, what will their final
velocity be? If they were 10m away from land, how long will they travel on the ice?
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11. A ball is released from rest and hits the floor for .1 seconds before bouncing up. If it
was dropped from 2 meters up:
a) What is the final velocity of the ball?
b) If the ball weighs .3N, what is the final velocity of the ball?
c) If the ball leaves the floor at 5m/s, what is the impulse given to the ball?
d) Was momentum conserved in this collision?
e) What object received the momentum the ball did not get?
f) If the Earth has a mass of 5.97x1024kg, what is its velocity after the collision? The
velocity will be close to zero.
12. A 200kg rocket is launched straight up at 50m/s.
a) What is the maximum height it reaches?
b) What is the rocket’s initial momentum?
c) What is the rocket’s final momentum? Was momentum conserved? Explain
why/why not.
d) At the top of its trajectory, the rocket explodes into two pieces. Once piece is 50kg
and is traveling at 45m/s. What is the mass and velocity of the other piece?
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