ACTIVIDAD: (dibuje la gráfica del movimiento de la tortuga) 1. Solo observando la fig 1 , indique cual es la velocidad instantánea de la tortuga a los 3,5 segundos. 2. Calcule la velocidad instantánea de la tortuga a los 6 segundos tomando el punto 2 cuando tes 10 s y \( X \) \( =3 \mathrm{~m} \) y el punto 1 cuando \( t \) es \( 4 \mathrm{~s} . \mathrm{y} X=-5 \mathrm{~m} \). 3. Por simple observación cual es la velocidad instantánea en los siguientes gráficos a los 5 segundos. (a) (b)
Added by Katie Y.
Close
Step 1
To determine the instantaneous velocity at 3.5 seconds, we need to find the slope of the tangent line to the curve at that point. Since we only have a figure and not an equation, we can estimate the slope by drawing a tangent line at 3.5 seconds and measuring its Show more…
Show all steps
Your feedback will help us improve your experience
Linda Hand and 51 other Precalculus educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The accompanying figure shows the position versus time curve for a certain particle moving along a straight line. Estimate each of the following from the graph: (a) the average velocity over the interval $0 \leq t \leq 3$ (b) the values of $t$ at which the instantaneous velocity is (c) the values of $t$ at which the instantancous velocity is either a maximum or a minimum (d) the instantaneous velocity when $t=3 \mathrm{s}$.
THE DERIVATIVE
Tangent Lines and Rates of Change
The accompanying figure shows the position versus time curve for a certain particle moving along a straight line. Estimate each of the following from the graph: (FIGURE CAN'T COPY) (a) the average velocity over the interval $0 \leq t \leq 3$ (b) the values of $t$ at which the instantaneous velocity is zero (c) the values of $t$ at which the instantaneous velocity is either a maximum or a minimum (d) the instantaneous velocity when $t=3 \mathrm{s}$
The Derivative
A turtle crawls along a straight line, which we will call the $x$-axis with the positive direction to the right. The equation for the turtle's position as a function of time is $x(t) =$ 50.0 cm + (2.00 cm/s)$t -$ (0.0625 cm/s$^2)t^2$. (a) Find the turtle's initial velocity, initial position, and initial acceleration. (b) At what time $t$ is the velocity of the turtle zero? (c) How long after starting does it take the turtle to return to its starting point? (d) At what times $t$ is the turtle a distance of 10.0 cm from its starting point? What is the velocity (magnitude and direction) of the turtle at each of those times? (e) Sketch graphs of $x$ versus $t, v_x$ versus $t$, and $a_x$ versus $t$, for the time interval $t =$ 0 to $t =$ 40 s.
Motion Along a Straight Line
Average and Instantaneous Acceleration
Recommended Textbooks
Precalculus with Limits
Precalculus
Watch the video solution with this free unlock.
EMAIL
PASSWORD