Question

read each scenario below and use the information given to calculate the average speed, distance or time. show your work.
a. a coach records the distance a runner travels during 3 different trials. what is the runners average speed in kilometers per minute?
trial 1 2 3
time (min) 4 3 6
distance (km) 1.0 0.75 1.5
b. a student records the distance traveled in the data table below. if the two turtles continue at the same speed, what is the average speed of both turtles?
1 2
time (s) 20 34
distance (m) 2.2 3.1
c. the distance traveled by a toy train over time is shown in the graph below. use the information in the graph to complete the table.
motion of toy train
time (s) 0 4 6
distance (m)
d. a student pushed a ball down a hill and recorded the distance, time and average speed during 3 different trials. how far did the ball travel with an average speed of 5.25 m/s?
trial 1 2 3
time (s) 5 4 8
distance (m) 15? 13
average speed (m/s) 3 5.25 1.625
e. a student walked to school at an average speed of 1.4 m/s. if the school is 1,250 meters away from their house, how long will it take for them to walk to school?
f. a cyclist traveled a distance of 22 miles in 1.23 hours. what was the average speed of the cyclist?

Explanation:

Step1: Recall speed - distance - time formula

The formula for speed is $v=\frac{d}{t}$, where $v$ is speed, $d$ is distance, and $t$ is time. We can re - arrange it to find $t=\frac{d}{v}$ and $d = v\times t$.

Step2: Solve problem E

Given $v = 1.4$ m/s and $d=1250$ m. Using $t=\frac{d}{v}$, we substitute the values: $t=\frac{1250}{1.4}\approx892.86$ s.

Step3: Solve problem F

Given $d = 22$ miles and $t = 1.23$ hours. Using $v=\frac{d}{t}$, we substitute the values: $v=\frac{22}{1.23}\approx17.89$ miles per hour.

Step4: Solve problem A

First, find the total distance: $d=1.0 + 0.75+1.5=3.25$ km and total time $t = 4 + 3+2=9$ min. Convert time to hours: $t=\frac{9}{60}=0.15$ h. Then, using $v=\frac{d}{t}$, $v=\frac{3.25}{0.15}\approx21.67$ km/h.

Step5: Solve problem B

For the first turtle: $v_1=\frac{d_1}{t_1}=\frac{2.2}{1}=2.2$ m/s. For the second turtle: $v_2=\frac{d_2}{t_2}=\frac{3.1}{2}=1.55$ m/s.

Step6: Solve problem C

We need to read values from the graph. At $t = 0$ s, $d = 4$ m; at $t = 4$ s, $d = 2$ m; at $t = 6$ s, $d = 0$ m.

Step7: Solve problem D

Using $d=v\times t$. For trial 1: $d_1=3\times5 = 15$ m. For trial 2: $d_2=2\times4 = 8$ m. For trial 3: $d_3=1\times8 = 8$ m.

Answer:

Problem E: Approximately 892.86 s
Problem F: Approximately 17.89 miles per hour
Problem A: Approximately 21.67 km/h
Problem B: First turtle: 2.2 m/s, Second turtle: 1.55 m/s
Problem C: At $t = 0$ s, $d = 4$ m; at $t = 4$ s, $d = 2$ m; at $t = 6$ s, $d = 0$ m
Problem D: Trial 1: 15 m, Trial 2: 8 m, Trial 3: 8 m