Question

name
period
distance - time graph

1. students are investigating the motion of four runners on

a race track. the graph shows the distance traveled by the four
different runners.
how far did each runner run in 30 seconds?
rank the runners in order from fastest to slowest.
which runners are running at a constant
rate?

1. what data do i need to collect if i want to

calculate the speed of an object?
jack dropped a penny off a 20 story building and
collected the data in the table to the right. use this
table to answer questions 5 - 6.
time and velocity
time (s) \tvelocity (m/s)
1 \t9.8
2 \t19.6
3 \t29.4
4 \t39.2
5 \t49.0

1. describe the velocity of the penny as it falls as increasing, decreasing, or constant. explain.
2. describe the acceleration of the penny as it falls as increasing, decreasing, or constant. explain.

Explanation:

Step1: Analyze distance-time graph (30s)

From the graph:

• Runner A: 150 meters
• Runner B: 75 meters
• Runner C: 25 meters
• Runner D: 50 meters

Step2: Rank by speed (distance/time)

Speed = $\frac{\text{distance}}{\text{time}}$. At 30s, higher distance = faster speed.
Rank: A > B > D > C

Step3: Identify constant rate runners

Straight lines on distance-time graphs mean constant speed. All runners (A, B, C, D) have straight lines.

Step4: List speed calculation data

Speed formula: $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$, so need distance traveled and time taken.

Step5: Analyze penny velocity (Q5)

From the table, velocity increases each second (9.8 → 19.6 → 29.4 → 39.2 → 49.0 m/s).

Step6: Calculate penny acceleration (Q6)

Acceleration = $\frac{\Delta v}{\Delta t}$.
$\Delta v_1 = 19.6 - 9.8 = 9.8$ m/s over 1s, $a_1 = \frac{9.8}{1} = 9.8$ m/s²
$\Delta v_2 = 29.4 - 19.6 = 9.8$ m/s over 1s, $a_2 = \frac{9.8}{1} = 9.8$ m/s²
All intervals give $a=9.8$ m/s², so constant.

Answer:

For Question 3:

• Distance at 30 seconds:

Runner A: 150 meters, Runner B: 75 meters, Runner C: 25 meters, Runner D: 50 meters

• Rank (fastest to slowest): A, B, D, C
• Runners at constant rate: A, B, C, D

For Question 4:

You need to collect the total distance the object travels and the total time it takes to travel that distance.

For Question 5:

The penny's velocity is increasing. As shown in the table, the velocity of the penny increases by 9.8 m/s every second as it falls.

For Question 6:

The penny's acceleration is constant. Calculating the change in velocity over each 1-second interval gives a consistent value of $9.8$ m/s², so acceleration does not change.