Instantaneous Velocity, Speed, and Position Derivatives

All flashcards

Instantaneous velocity

The limit of average velocity as the time interval approaches zero; it is the derivative of position with respect to time.

Instantaneous speed

The magnitude, or absolute value, of instantaneous velocity.

Average speed

Total distance traveled divided by elapsed time.

Average velocity

Displacement divided by elapsed time.

Position–time graph slope

The slope at a point gives instantaneous velocity; the slope between two points gives average velocity.

Quiz questions

1. For $x(t)=(2.0\,\text{m/s})t+(0.25\,\text{m/s}^3)t^3$, what is the velocity function?Answer: $v(t)=2.0\,\text{m/s}+(0.75\,\text{m/s}^3)t^2$
2. For $x(t)=(4.0\,\text{m/s})t-(1.0\,\text{m/s}^2)t^2$, what is the instantaneous velocity at $t=1.0\,\text{s}$?Answer: $2.0\,\text{m/s}$
3. An object's position is $2\,\text{m}$ at $t=1\,\text{s}$ and $11\,\text{m}$ at $t=4\,\text{s}$. What is its average velocity over that interval?Answer: $3\,\text{m/s}$
4. At a particular time, an object is at position $-5\,\text{m}$ and its position–time graph has slope $+1.5\,\text{m/s}$. What is its velocity?Answer: $+1.5\,\text{m/s}$
5. For $x(t)=(3.0\,\text{m/s})t-(3.0\,\text{m/s}^2)t^2$, at what time does the velocity become zero?Answer: $0.50\,\text{s}$