Question

section 4.2

1. oliver is warming up for a track meet. first he walks 1 m/s for 100 seconds. then he runs at 3 m/s for 200 seconds. his shoe comes untied, so he stops for 20 seconds to tie it. finally he runs at 4 m/s for 200 seconds.

a. draw a position vs. time graph of olivers motion. hint: use the table below to calculate olivers position during each part during his warm up.
b. draw a speed vs. time graph of olivers motion.
c. what is the total distance that oliver travels?
d. what is olivers average speed during his 520 second warm - up?
speed (m/s) x time (s) = position (m)

Explanation:

Step1: Calculate distance for each part

For the first - part: He walks at a speed of $v_1 = 1$ m/s for $t_1=100$ s. Using the formula $d = v\times t$, the distance $d_1=v_1\times t_1 = 1\times100 = 100$ m.

Step2: Calculate distance for the second - part

He runs at a speed of $v_2 = 3$ m/s for $t_2 = 200$ s. Using the formula $d = v\times t$, the distance $d_2=v_2\times t_2=3\times200 = 600$ m.

Step3: Calculate distance for the third - part

He stops for $t_3 = 20$ s, so the distance $d_3 = 0$ m (since $v_3=0$ m/s).

Step4: Calculate distance for the fourth - part

He runs at a speed of $v_4 = 4$ m/s for $t_4 = 200$ s. Using the formula $d = v\times t$, the distance $d_4=v_4\times t_4=4\times200 = 800$ m.

Step5: Calculate the total distance

The total distance $D=d_1 + d_2+d_3 + d_4=100 + 600+0 + 800=1500$ m.

Step6: Calculate the average speed

The total time $T = 100+200 + 20+200=520$ s. Using the formula $v_{avg}=\frac{D}{T}$, the average speed $v_{avg}=\frac{1500}{520}\approx2.88$ m/s.

Answer:

c. The total distance Oliver travels is 1500 m.
d. Oliver's average speed during his 520 - second warm - up is approximately 2.88 m/s.

(Note: Drawing the position - vs - time and speed - vs - time graphs requires graph - making tools. For the position - vs - time graph, the graph will have linear segments with slopes corresponding to the speeds in each part and horizontal segments for the rest period. For the speed - vs - time graph, it will have horizontal segments at the given speeds for the respective time intervals and a horizontal segment at 0 for the rest period.)