Question

instructions: the data tables and graphs (problems 4-6) will need to go on a piece of graph paper. staple it all together. show all work!!! problem 4: write the following chart onto your paper. use the given information to fill in the rest of the chart. hints on how to calculate the blank cells are in blue. show your work on how you are calculating each value.

time (s)	position (m)	velocity (m/s)	acceleration (δv/δt)
2	0.5	= d₂ - d₁ / t₂ - t₁	na
3	1	= d₃ - d₂ / t₃ - t₂	= v₃ - v₂ / t₃ - t₂
4	2.1
5	3.8

problem 5: create a distance versus time graph using the information above. problem 6: create a velocity versus time graph using the information above. optional additional practice: write your own acceleration problems requiring unit conversion.

Explanation:

Step1: Calculate velocity for row 2

Using the formula $v=\frac{d_2 - d_1}{t_2 - t_1}$, where $d_1 = 0.2$, $d_2=0.5$, $t_1 = 1$, $t_2 = 2$.
$v=\frac{0.5 - 0.2}{2 - 1}=\frac{0.3}{1}=0.3$ m/s

Step2: Calculate velocity for row 3

Using the formula $v=\frac{d_3 - d_2}{t_3 - t_2}$, where $d_2 = 0.5$, $d_3 = 1$, $t_2 = 2$, $t_3 = 3$.
$v=\frac{1 - 0.5}{3 - 2}=\frac{0.5}{1}=0.5$ m/s

Step3: Calculate velocity for row 4

Using the formula $v=\frac{d_4 - d_3}{t_4 - t_3}$, where $d_3 = 1$, $d_4 = 2.1$, $t_3 = 3$, $t_4 = 4$.
$v=\frac{2.1 - 1}{4 - 3}=\frac{1.1}{1}=1.1$ m/s

Step4: Calculate velocity for row 5

Using the formula $v=\frac{d_5 - d_4}{t_5 - t_4}$, where $d_4 = 2.1$, $d_5 = 3.8$, $t_4 = 4$, $t_5 = 5$.
$v=\frac{3.8 - 2.1}{5 - 4}=\frac{1.7}{1}=1.7$ m/s

Step5: Calculate acceleration for row 3

Using the formula $a=\frac{v_3 - v_2}{t_3 - t_2}$, where $v_2 = 0.3$, $v_3 = 0.5$, $t_2 = 2$, $t_3 = 3$.
$a=\frac{0.5 - 0.3}{3 - 2}=\frac{0.2}{1}=0.2$ m/s²

Step6: Calculate acceleration for row 4

Using the formula $a=\frac{v_4 - v_3}{t_4 - t_3}$, where $v_3 = 0.5$, $v_4 = 1.1$, $t_3 = 3$, $t_4 = 4$.
$a=\frac{1.1 - 0.5}{4 - 3}=\frac{0.6}{1}=0.6$ m/s²

Step7: Calculate acceleration for row 5

Using the formula $a=\frac{v_5 - v_4}{t_5 - t_4}$, where $v_4 = 1.1$, $v_5 = 1.7$, $t_4 = 4$, $t_5 = 5$.
$a=\frac{1.7 - 1.1}{5 - 4}=\frac{0.6}{1}=0.6$ m/s²

The completed table:

Time (s)	Position (m)	Velocity (m/s)	Acceleration ($\Delta v/\Delta t$)
2	0.5	0.3	NA
3	1	0.5	0.2
4	2.1	1.1	0.6
5	3.8	1.7	0.6

Answer:

The completed table is shown above.