Question

1-17 graphing position vs. time to find velocity
name kiaia green mr. dimitriou
period 5th date 10/1/25
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 slope formula

The slope formula for a position - time graph (which is also the formula for average velocity) is $v=\frac{\Delta x}{\Delta t}=\frac{x_f - x_0}{t_f - t_0}$.

Step2: Calculate slope between 0 and 1 seconds

Given $x_0 = 2$ m at $t_0=0$ s and $x_f = 7$ m at $t_f = 1$ s. Then $v=\frac{x_f - x_0}{t_f - t_0}=\frac{7 - 2}{1-0}$.
$v=\frac{5}{1}=5$ m/s.

Step3: Calculate average velocity between 0 and 3 seconds

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

Step4: Calculate average velocity between 2 and 3 seconds

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

Answer:

1. 5 m/s
2. 5 m/s
3. 4 m/s
4. 6 m/s