Average velocity The graph gives the position s(t) of an...

Average velocity The graph gives the position $s(t)$ of an object moving along a line at time $t,$ over a 2.5 -second interval. Find the average velocity of the object over the following intervals.
a. [0.5,2.5]
b. [0.5,2]
c. [0.5,1.5]
d. [0.5,1]
(FIGURE CANNOT COPY)

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Time Interval

A time interval is defined by two endpoints [t1, t2] and represents the duration over which the displacement is measured. Correct identification of the interval is essential, as it directly affects the calculation of average velocity by determining the denominator in the difference quotient.

Displacement

Displacement refers to the net change in the object's position, computed as the difference between the final and initial positions. It is a vector quantity that, when divided by the time interval, gives the average velocity.

Position Function

The position function, usually denoted as s(t), describes the location of an object along a line at any time t. It is fundamental in kinematics because it allows for the determination of displacement, velocity, and acceleration by analyzing the function’s values and derivatives over time.

Average Velocity

Average velocity is defined as the total displacement divided by the total time elapsed. It quantifies the overall rate at which an object’s position changes over a given time interval, and is calculated by taking the difference of the position function's values at the endpoints of the interval and dividing by the time difference.

Transcript

Please give Ace some feedback