From the position-time graph, we have the following:
Distance covered Time
0 to 28 m 0 to 20 seconds
28m to 52 m 20 to 60 seconds
At 52 m 60 to 80 seconds
52 to -20m 80 to 110 seconds
Let's find the average speed for the entire trip.
To find the average speed, apply the formula:
[tex]avg\text{ spe}ed=\frac{total\text{ distance}}{total\text{ time}}[/tex]Distance at line 1: 28 - 0 = 28m
Distance at line 2: 52 - 28 = 24 m
Distance at line 3: 0 m
Distance at line 4: -20m - 52 = -72 m
Thus, we have the equation:
[tex]s=\frac{d_1}{t_1}+\frac{d_2}{t_2}+\frac{d_3}{t_3}+\frac{d_4}{t_4}[/tex]Where:
d1 = 28 m
d2 = 24 m
d3 = 0 m
d4 = 72 m
t = 110 s
Now substitue values into the equation:
[tex]\begin{gathered} s=\frac{28}{20}+\frac{24}{40}+\frac{0}{20}+\frac{72}{30} \\ \\ s=4.4\text{ m/s} \end{gathered}[/tex]Therefore, the average speed for the trip is 4.4 m/s.
ANSWER:
Equation:
[tex]s=\frac{d_1}{t_1}+\frac{d_2}{t_2}+\frac{d_3}{t_3}+\frac{d_4}{t_4}[/tex]Substitution:
[tex]s=\frac{28}{20}+\frac{24}{40}+\frac{0}{20}+\frac{72}{30}[/tex]Calculation:
[tex]\begin{gathered} s=1.4\text{ + }0.6\text{ + 0 + }2.4 \\ \\ s=4.4\text{ m/s} \end{gathered}[/tex]