1D Motion

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Terms and Formulae

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Terms and Formulae

Terms

Kinematics

Kinematics is concerned with describing the way in which objects move.
Displacement

An objects total change in position. If a man runs around an oval 400 meter track, stopping at the precise location he began, though he ran a distance of 400 meters, his total displacement was 0.
Dynamics

Dynamics focuses on understanding why objects move the way they do.
Reference frame

The coordinate system with respect to which motion is being described.
Speed

A measure of how fast an object is moving.
Average velocity

The time-average of the velocity function over a specified time-interval. (See formula below.)
Instantaneous velocity

The value of the velocity function at a particular instant in time. (See formula below.)
Gravitational acceleration

The graviational acceleration of objects near the earth's surface is the same for all objects regardless of mass and is given by the number g = 9.8m/s².
Scalar-valued function

A function that outputs scalars (regular numbers). Most common functions that you are probably familiar with are scalar-valued functions.
Vector-valued function

A function that outputs vectors. This means that while the domain of the function may consist of scalars, the values in the range are all vectors.
Position function

A position function can be either scalar-valued (for motion in one dimension) or vector-valued (for motion in two or three dimensions). At each point in time its value represents the position of an object at that time.
Velocity function

This function is the time-derivative of the position function, and gives the velocity of an object at each point in time.
Acceleration function

This function is the time-derivative of the velocity function, and the second time-derivative of the position function. It gives the value of the acceleration of an object at each point in time.
Time-derivative

The time-derivative of a function is a new function whose value at each point represents the rate of change of the original function with respect to time.
Simple harmonic motion

Periodic motion that can be described by special types of position functions. Examples of simple harmonic motion include an object moving in a circle and a ball bouncing up and down on a spring.

Formulae

The average velocity for an object with position function x(t) over the time interval (t₀, t₁).

v_avg =

The instantaneous velocity at time t for an object with position function x(t).

v(t) =

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