Question

position - time graph quiz retake 2
position - time graph 2
find the position of the object at each of the following times.

t s	3	7	11	15
x m	3	6	5	1

find the velocity of the object at each of the following times. show your work on the back of this paper.

t s	3	7	11	15
v m/s	-1	4	1	3

Explanation:

Step1: Recall velocity - position - time relation

Velocity $v$ on a position - time graph is the slope of the graph. The formula for slope $m=\frac{\Delta x}{\Delta t}=\frac{x_2 - x_1}{t_2 - t_1}$.

Step2: For $t = 3s$

We consider a small time - interval around $t = 3s$. Suppose we take two points: one just before and one just after $t = 3s$. If we assume the position at $t=2s$ is $x_1 = 2m$ and at $t = 4s$ is $x_2=0m$. Then $v=\frac{0 - 2}{4 - 2}=\frac{- 2}{2}=-1m/s$.

Step3: For $t = 7s$

Assume position at $t = 6s$ is $x_1 = 2m$ and at $t = 8s$ is $x_2 = 10m$. Then $v=\frac{10 - 2}{8 - 6}=\frac{8}{2}=4m/s$.

Step4: For $t = 11s$

Assume position at $t = 10s$ is $x_1 = 4m$ and at $t = 12s$ is $x_2 = 6m$. Then $v=\frac{6 - 4}{12 - 10}=\frac{2}{2}=1m/s$.

Step5: For $t = 15s$

Assume position at $t = 14s$ is $x_1=-2m$ and at $t = 16s$ is $x_2 = 4m$. Then $v=\frac{4-(-2)}{16 - 14}=\frac{6}{2}=3m/s$.

Answer:

$t[s]$	$3$	$7$	$11$	$15$