Kinematics

The position of an object

is a vector that describes the object's location with respect to some agreed-upon coordinate origin

The total distance from the origin

is the magnitude of the position vector, which is obtained just like we find the hypotenuse of a triangle - by taking the root of the sum of the squares of the side lengths

The magnitude of velocity

speed

Kinematics

study of motion

Find velocity from position vector

take the derivative

Displacement

the change in position of an object

direction

the path that a moving object follows vector quantity

Velocity

the speed of an object in a particular direction

What is the average velocity of a race car that does exactly 440 laps around a one mile circuit in 4.0 hours? What is the magnitude of the average velocity? What is the average speed of the race car?

zero vector, zero, 110 mph

Magnitude equation

|r| = sqrt( rx^2 + ry^2 +rz^2 )

Give estimates of how fast you can run, how fast a car drives on the freeway and how fast jet planes fly in meters per second.

8m/s; 30m/s; 300m/s

Law of Inertia

A law formulated by Galileo that states that motion, not rest, is the natural state of an object, and that an object continues in motion forever unless stopped by some external force.

Newton's First Law

An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. Equate to the law of inertia

When a comet is far from other objects, what can we say about its velocity? Its position? Its acceleration?

Constant velocity, potentially changing position, zero acceleration

Air drag

Frictional resistance due to motion through air depend quadratically on velocity

magnitude

Greatness of size, strength, or importance scalar quantity

viscous drag

The force that opposes the motion of an object through a liquid depends linearly on velocity

Do any of these answers change if the ball additionally has a horizontal component to its initial velocity?

No, because kinematics in x and y directions are independent according to all the equations, and acceleration due to gravity is only in the y-direction.

Two types of resistance that objects experience when moving through fluids

Viscous drag, Air drag