Question

position - time graph qul retare 9
position - time graph 3
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 at a given time. The slope $m$ between two points $(t_1,x_1)$ and $(t_2,x_2)$ is calculated as $m=\frac{x_2 - x_1}{t_2 - t_1}$.

Step2: For $t = 3s$

Let's consider two nearby points. Suppose we take a small time - interval around $t = 3s$. If we consider the points $(2,x(2))$ and $(4,x(4))$ from the position - time graph. Let $x(2)=4m$ and $x(4)=2m$. Then $v=\frac{2 - 4}{4 - 2}=\frac{- 2}{2}=-1m/s$.

Step3: For $t = 7s$

Consider points around $t = 7s$. Let's take $(6,x(6))$ and $(8,x(8))$. Suppose $x(6)=2m$ and $x(8)=6m$. Then $v=\frac{6 - 2}{8 - 6}=\frac{4}{2}=2m/s$.

Step4: For $t = 11s$

Take points around $t = 11s$. Let $(10,x(10))$ and $(12,x(12))$. Suppose $x(10)=4m$ and $x(12)=5m$. Then $v=\frac{5 - 4}{12 - 10}=\frac{1}{2}=1m/s$.

Step5: For $t = 15s$

Take points around $t = 15s$. Let $(14,x(14))$ and $(16,x(16))$. Suppose $x(14)=-2m$ and $x(16)=4m$. Then $v=\frac{4-(-2)}{16 - 14}=\frac{6}{2}=3m/s$.

Answer:

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