a position - time graph for a particle moving along the x axis is shown in the figure below.\n(a) find the…

a position - time graph for a particle moving along the x axis is shown in the figure below.\n(a) find the average velocity in the time interval t = 2.00 s to t = 4.00 s. (indicate the direction with the sign of your answer.) m/s\n(b) determine the instantaneous velocity at t = 2.00 s by measuring the slope of the tangent line shown in the graph. (note that t = 2.00 s is where the tangent line touches the curve. indicate the direction with the sign of your answer.) m/s\n(c) at what value of t is the velocity zero? s

a position - time graph for a particle moving along the x axis is shown in the figure below.\n(a) find the average velocity in the time interval t = 2.00 s to t = 4.00 s. (indicate the direction with the sign of your answer.) m/s\n(b) determine the instantaneous velocity at t = 2.00 s by measuring the slope of the tangent line shown in the graph. (note that t = 2.00 s is where the tangent line touches the curve. indicate the direction with the sign of your answer.) m/s\n(c) at what value of t is the velocity zero? s

Answer

Explanation:

Step1: Recall average - velocity formula

The average velocity formula is $v_{avg}=\frac{\Delta x}{\Delta t}$, where $\Delta x = x_f - x_i$ and $\Delta t=t_f - t_i$.

Step2: Determine $x_i$, $x_f$, $t_i$, $t_f$ from the graph

For the time - interval $t = 2.00\ s$ to $t = 4.00\ s$, from the position - time graph, when $t_i=2.00\ s$, $x_i$ (read from the graph) is approximately $2\ m$, and when $t_f = 4.00\ s$, $x_f$ is approximately $1\ m$.

Step3: Calculate $\Delta x$ and $\Delta t$

$\Delta x=x_f - x_i=1 - 2=- 1\ m$ and $\Delta t=t_f - t_i=4 - 2 = 2\ s$.

Step4: Calculate average velocity

$v_{avg}=\frac{\Delta x}{\Delta t}=\frac{-1}{2}=-0.5\ m/s$.

Step5: Recall instantaneous - velocity concept

The instantaneous velocity at a point on a position - time graph is the slope of the tangent line at that point. For $t = 2.00\ s$, measure the slope of the tangent line. The tangent line at $t = 2.00\ s$ has two points: Let's assume two points on the tangent line are $(t_1,x_1)=(1,3)$ and $(t_2,x_2)=(3,1)$. The slope $m=\frac{x_2 - x_1}{t_2 - t_1}=\frac{1 - 3}{3 - 1}=\frac{-2}{2}=-1\ m/s$.

Step6: Find when velocity is zero

The velocity is zero when the slope of the position - time graph is zero. This occurs when the tangent line to the curve is horizontal. From the graph, this happens at approximately $t = 6\ s$.

Answer:

(a) $-0.5\ m/s$ (b) $-1\ m/s$ (c) $6\ s$