Review: Position, Velocity, Acceleration, Inc/Dec, Extrema

Front

What is the definition of position in physics?

Back

Position refers to the location of an object at a particular point in time, often represented as a function of time, s(t).

Front

How is velocity defined in relation to position?

Back

Velocity is the rate of change of position with respect to time, mathematically defined as v(t) = s'(t).

Front

What is the formula for calculating instantaneous velocity?

Back

Instantaneous velocity can be calculated using the derivative of the position function: v(t) = lim (Δt -> 0) [s(t + Δt) - s(t)] / Δt.

Front

What does it mean when a particle is at rest?

Back

A particle is at rest when its velocity is zero, i.e., v(t) = 0.

Front

What is acceleration in relation to velocity?

Back

Acceleration is the rate of change of velocity with respect to time, defined as a(t) = v'(t).

Front

How can you determine when a particle changes direction?

Back

A particle changes direction when its velocity changes sign, which occurs at points where v(t) = 0.

Front

What are critical values in calculus?

Back

Critical values are points in the domain of a function where the derivative is zero or undefined, indicating potential extrema.

Front

What is the significance of the first derivative test?

Back

The first derivative test helps determine whether a critical point is a local maximum, local minimum, or neither by analyzing the sign of the derivative before and after the point.

Front

What does it indicate when f'(x) changes from negative to positive?

Back

When f'(x) changes from negative to positive, it indicates that there is a local minimum at that point.

Front

What is the formula for finding the velocity function from a position function s(t)?

Back

The velocity function can be found by taking the derivative of the position function: v(t) = s'(t).