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AP Physics C Exam Review #1: Kinematics & Newton’s Laws

One Dimensional Motion

• Given a graph of position, velocity, or acceleration versus time, be able to describe the motion of an

object, and sketch graphs of the other two quantities.

o If velocity is constant, then the change in the position is constant and acceleration is zero

o If velocity is positive and increasing, then change in position is exponentially increasing, and

acceleration is positive

• Given a function of position, velocity, or acceleration in terms of time, be able to determine thefunctions of the other two quantities

( ) ( )d v t x t dt = ( ) ( )d a t v t

dt = ( ) ( )x t v t dt = ∫ ( ) ( )v t a t dt = ∫

• Constant Acceleration Equations

21

2ix v t at ∆ = +

1( )

2i f x v v t ∆ = + 2 2 2f iv v a x= + ∆ f i

v v at = +

Two Dimensional Motion

• NEVER do calculations with the overall velocity of a projectile, ALWAYS resolve into components anduse 1-D motion relationships from above

0cosxv v= θ

0 0siny

v v θ =

• Time of flight depends on the y-component of the motion, unless you are trying to find a height at a

given distance

2

0

1

2yy v t gt ∆ = +

0

1( )

2y f y v v t ∆ = + 2 2

02fy y

v v g y= + ∆0fy yv v gt = +



Newton’s Laws of Motion (Forces)

Newton’s 1 st Law

• Objects in motion want to continue to remain in straight-line motion, and objects at rest want to remain

at rest

• The Law of Inertia

Newton’s 2 nd Law

• The acceleration of an object is directly proportional to the force applied to the object, and inverselyproportional to the mass of the object

• F = ma

Summation Equations

• When forces act upon an object, the sum of these forces must be added as vectors because force is avector quantity

• These equations will represent either the vertical or the horizontal, and only will be at an angle if we are

discussing “blocks on ramps”

• The sum of the equations will always be either ma (from Newton’s 2nd law) or 0, if the object is at

equilibrium

Equilibrium

• When the net force acting upon and object is 0, the object is said to be at equilibrium.

• Two types of equilibrium:

o Static

Object remains at rest

o Kinetic

Object moves at a constant velocity

Constant Forces

• When a constant force is applied to an object, the object will be accelerating at a constant rate

F ma=Variable Forces

• As you remember from the discussion of momentum last semester, the integral of a variable force over

time is equal to the impulse experienced by the object

( )J m v F t dt = ∆ = ∫

• Therefore, if you want to determine the change in the object’s velocity, simple divide the impulse by the

object’s mass. SIMPLE!!!

Frictional Forces

• Frictional forces always oppose the direction of an object’s motion

• The frictional force between an object and the surface it rests upon is equal to the product of the

coefficient of friction and the normal force of the object

f N F F µ =



• Static Friction

o The friction that must be overcome for an object to begin motion

o The coefficient of static friction is used

o When one is asked to determine the coefficient of static friction, set the applied force equal to the

friction equation and solve for S µ

app s N F F µ =• Kinetic Friction

o The friction that opposes an object sliding

o The coefficient of kinetic friction is used

Blocks on Ramps

• When a block is placed on a ramp, its tendency is to accelerate down the ramp at a fraction of gravity

• If you’ll remember from all of your studies of blocks on ramps, you should label the diagram with all of the following forces

o Parallel force ( sinII F mg θ = )

o Gravitational force ( GF mg = )o Normal force ( cosN F mg θ = )

o Frictional force, if present ( f N F F µ = )

Newton’s 3 rd Law

• For every action, there is an equal and opposite reaction

• FORCE PAIRS!!!

• Especially important when dealing with blocks stacked on each other where friction is present

o The force of friction is the SAME between the two

Two or More Objects Connected• When objects are connected via a massless or light rope, the objects will accelerate at the same rate, and

the tension force present on the rope is constant throughout

• If connected over a frictionless, massless pulley, no torque must be taken into account

• Use parallel equations and either add or use substitution to solve for the unknown needed, usually

acceleration or tension force

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