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Equations
Definitions
Differences
Miscellaneous
Problem Solving
100

X-Component and Y-component we use for magnitude (and other) equations 

Ax = A * sin(theta)

Ay = A * cos(theta)

100
A physical measurement that contains directional information
Vector quantity
100
Speed vs Velocity
Speed is the time rate of change of the distance traveled by an object, whereas velocity is the time rate of change of an object's position (displacement).
100
On the moon, gravity is less than on earth. What would the acceleration on the moon be compared to earth's acceleration due to gravity?
Acceleration on the moon would be less than acceleration on earth.
100

A cart rolls uninhibited across the parking lot in a straight line at 2.3 m/sec. If the cart rolls for 15.3 minutes, how far has it traveled?

v = dx/dt 

dx = 2100m (or 2.1 * 10^3 m)

200

Magnitude and Direction

Magnitude = sqrt (Ax^2 + Ay^2)

Direction = tan^-1 (Ay/Ax)

200
The time rate of change of an object's velocity
Acceleration
200
Instantaneous Velocity vs Average Velocity
Instantaneous velocity is the velocity of an object at one moment in time, whereas average velocity is the velocity of an object over an extended period of time.
200
When an object is thrown straight up in the presence of gravity, when will it reach its max height?
When the object's velocity is zero
200

A biker is riding at 25 m/sec and stops in 0.103 km. What was the deceleration provided by the brakes?

v^2 = v0^2 + 2a * dx

a = -3.0 m/sec^2

300

Range

range = v0^2 * sin(2*theta) 

            ________________ 

                    g

300
The motion of an object when it is falling solely under the influence of gravity
Freefall
300
Slope of a position-versus-time curve vs. Slope of a velocity-versus-time curve
The slope of a position-versus-time curve is velocity. The slope of a velocity-versus-time curve is acceleration.
300
If a projectile (in 2 dimensions) lands at the height from which it was launched, what is its final speed?
The same as its initial speed
300

A vector A has a magnitude of 34.0 m/sec and a direction of 45 degrees. Find its x and y components.

Ax = 34.0 m/sec * cos (45) = 24 m/sec

Ay = 34.0 m/sec * sin (45) = 24 m/sec

400

Relates Velocity, Acceleration, and Time

v = v0 + at

400
The velocity a falling object has when, due to air resistance, its acceleration is reduced to zero. This is the maximum velocity a falling object subject to air resistance can achieve.
Terminal Velocity
400

Acceleration due to gravity (feet vs meters)

9.8 m/sec^2 

32 ft/sec^2

400
Explain how to graphically add two vectors
Take the tail of the 2nd vector and place it at the head of the 1st vector. The vector that then completes the triangle by starting at the tail of the first and pointing to the head of the second represents the sum of the two vectors.
400

A sailor wants to destroy an enemy base 7512 meters away from his position. The base is at the same elevation as the sailor. If the ship's cannon fires missiles with an initial speed of 345 m/sec, at what angle should the sailor aim the launcher?

Using the range equation, theta = 19 degrees

500

Relates Displacement, Velocity, Acceleration, and Time

dx = v0t + .5at^2

500
Motion that occurs when an object moves in two dimensions but has zero acceleration in one of those dimensions and a constant, non-zero acceleration in the other.
Parabolic motion
500

Calculating direction in quadrants I, II, III, IV

Quadrant I - do nothing

Quadrant II - add 180 degrees

Quadrant III - add 180 degrees

Quadrant IV - add 360 degrees

500
What have we ignored in every equation?
Air resistance
500
A captain steers his ship with a velocity of 125 mph at a heading of 30.0 degrees. If the current is flowing southwest at 225 degrees at 20 mph, what is the ship's final velocity? Ship: Vx = 108 mph; Vy = 62.5 mph Current: Vx = -14.1 mph; Vy = -14.1 mph
106 mph at 27 degrees