MCAT Physics Flashcard 2012

KinematicsUnits and Dimensionsc = centi = 10^-xm = mili = 10^-xµ = micro = 10 ^-xn = nano = 10^-xp = pico= 10^-xG/B = giga = 10^xM = mega = 10^xk = kilo = 10^x

KinematicsKinematicsKinematics is the description of motion in terms of an object's position, velocity, and acceleration.
Displacement (Δx) is the change in _____;It is a ____ quantity. Displacement does not depend on the path between the initial and final points.
The average velocity is also a vector quantity and takes the same direction as Δx. Velocity tells us how fast an object's position.
V = Δx/Δt
Velocity changes if the speed or direction changes.
Average Speed = total distance traveled divided by the time = d/Δt and is a scalar quantity and has no direction.

KinematicsKinematicsVelocity tells us how fast and object's position changes; acceleration tells us how fast an object's _____ changes. *If velocity is changing, then there is acceleration. If acceleration points in the same direction as the initial velocity, then the object's speed is _____. If the acceleration points in the direction opposite to the initial velocity, then the object's speed is _____.
acceleration = Δv/Δt

KinematicsUniformly Accelerated MotionIn uniformly accelerated motion, acceleration is constant. v =v₀ + at
Δx = 1/2(v₀ + v)t
Δx = v₀t + 1/2at²
Δx = vt - 1/2at²
v² = v₀² +2ad + 1/2at²
In free fall, weight = gravity and acceleration = 9.8 m/s

KinematicsKinematics with GraphsWhen plotting Δx vs. Δt, the slope is the ____. And when plotting Δv vs. Δ t, the slope is the ____. The area under a velocity vs. time graph gives the displacement.
Free FallIn free fall there is constant acceleration.
g = acceleration due to gravity

KinematicsProjectile MotionAn object experiencing only the constant, downward acceleration due to gravity (free fall) is called projectile motion and the path will be a ____. Unlike linear motion, in projectile motion velocity and position components are in both the vertical and horizontal directions thus must be analyzed separately.
Horizontal MotionDisplacement: x = V_0xtVelocity: v_x =v₀ (constant)Acceleration: a_x = 0 V_0x = V Cosθ
Vertical MotionDisplacement: y = v₀t + 1/2 (-g)t²Velocity: v_y = v_0y + (-g)tAcceleration: a_y = -g V_0y = V sinθ
tan θ = R_y/ R_xtan^-1 (y/x) = θ
*If the horizontal acceleration is zero throughout the projectile's flight motion then the horizontal velocity will be constant throughout the flight*If the horizontal velocity does not change then whatever it was initially is all it will ever be.

KinematicsKinematicsWhen solving a problem with vectors going in different directions, break each down into their x and y components.
Ex: ↖ A =8N ↗B = 4N ↘ C= 8 N θ= 30°
A_x = -8 cos 30 B_x = 4 cos 30 C_x = 8 cos 30_Ay = - 8 sin 30 B_y = 4 sin 30 C_y = -8 sin 30
To find the resultant add all components of R_x and R_y. The magnitude of the resultant = √R_x² + R_y²

MCAT MATHLaws of Exponentsb^p x b^q =
b^p / b^q =
(b^p)^q =
b⁰ =
b^-p =
(ab)^p =
(a/b)^p =

MCAT MATHLaws of Radicals√ab =

√a/b =

^p√a^p =

MCAT MATHThe X-Plane, Y-Plane and other GraphsLines ~KinematicsThe equation of a line is: y = mx + b m = slope b = y-intercept

MCAT MATHThe X-Plane, Y-Plane and other GraphsParabolas y = kx² The general form of the equation of a parabola is
a (x-h)² +k
The parabola opens upward if a is ____; if it opens downward if a is ____. The vertical line of symmetry passes through the ____.

1. The vertex of the parabola is (h, k).
2. 
   

MCAT MATHThe X-Plane, Y-Plane and other GraphsParabolasThe exponential decay curve has the following equation:
y = Ae^-kx
It intersects the y-axis at (0, A) and as x increases, y decreases.

MCAT MATHThe X-Plane, Y-Plane and other GraphsParabolasThe hyperbola graph has the following equation:y = k/x
It is the graph of inverse proportions: for small values of x, the values of y are large and vice versa.

MCAT MATHTrigonometry: Pythagorean Theorem The pythagorean triple is referred to as the 3, 4, 5 triangle. Any multiple of this triangle is considered a pythagorean triple.
Sin θ= opp/hypcos θ= adj/ hyptan θ= opp/ adj

MCAT MATHTrigonometry: Right TrianglesFor an isosceles Right Triangle (2 congruent sides) Both sides are equal to x and hypotenuse = x√2
sin 45 = 1/√2 cos 45 = 1/√2 tan 45 = 1
For a 30-60-90 triangle: short leg= x; long leg = x√3; hypotenuse = 2x
sin 30 = 1/2 sin 60 = √3/ 2
cos 30 = √3/ 2 cos 60 = 1/2
tan 30 = 1√3 or √3 /3 tan 60 = √3