Question

1-17 graphing position vs. time to find velocity
name kiara green mr. dimitriou period 5th date 10/11/25
assume all distances are in a straight line unless otherwise specified.

1. draw the following position vs. time graph. remember, in physics time is always the independent variable (that means the line that goes sideways on the graph)

t (seconds) x (meters)
0 2
1 7
2 8
3 14
4 30
5 28
remember, velocity is change in position over change in time $\frac{xf - x0}{tf - t0}$

1. look at the table above. what is the slope of the graph between 0 and 1 seconds?
2. what was the average velocity between 0 and 1 seconds?
3. what was the average velocity between 0 and 3 seconds?
4. what was the average velocity between 2 and 3 seconds?

Explanation:

Step1: Recall average - velocity formula

The formula for average velocity is $v=\frac{x_f - x_0}{t_f - t_0}$, where $x_f$ and $x_0$ are final and initial positions respectively, and $t_f$ and $t_0$ are final and initial times respectively.

Step2: Calculate average velocity between 0 and 3 seconds

We have $x_0 = 2$ m at $t_0=0$ s and $x_f = 14$ m at $t_f = 3$ s.
$v=\frac{14 - 2}{3-0}=\frac{12}{3}=4$ m/s

Step3: Calculate average velocity between 2 and 3 seconds

We have $x_0 = 8$ m at $t_0 = 2$ s and $x_f = 14$ m at $t_f = 3$ s.
$v=\frac{14 - 8}{3 - 2}=\frac{6}{1}=6$ m/s

Answer:

1. For average velocity between 0 and 3 seconds: 4 m/s
2. For average velocity between 2 and 3 seconds: 6 m/s