Question

activity c (continued from previous page)

1. in the gizmo, create a position - time graph of a runner with these characteristics:

• travels a distance of 60 yards in 4 seconds
• has a displacement of +10 yards

sketch your graph on the blank axes to the right.

1. look at the graph you made in question 4. think about the speed of that runner.

a. what was the runner’s speed for the first 2 seconds? ____________
b. what was the runner’s speed for the last 2 seconds? ____________
c. what was the runner’s average speed over all 4 seconds? ____________

1. now think about the velocity of the runner in question 4.

a. what was the runner’s velocity for the first 2 seconds? ____________
b. what was the runner’s velocity for the last 2 seconds? ____________
c. what was the runner’s average velocity over all 4 seconds? ____________

1. suppose you knew the time, displacement, and total distance traveled for a runner.

a. how would you calculate the runner’s average speed? ____________
b. how would you calculate the runner’s average velocity? ____________

Explanation:

Step1: Recall speed formula

Speed = $\frac{\text{distance}}{\text{time}}$

Step2: Calculate average speed over 4 - seconds

Given distance = 60 yards, time = 4 seconds. Average speed = $\frac{60}{4}=15$ yards/second. Since we have no information about non - uniform motion in the first 2 and last 2 seconds, assume uniform motion. So speed in first 2 seconds and last 2 seconds is also 15 yards/second as average speed is 15 yards/second for the whole 4 - second interval.

Step3: Recall velocity formula

Velocity = $\frac{\text{displacement}}{\text{time}}$

Step4: Calculate average velocity over 4 - seconds

Given displacement = 10 yards, time = 4 seconds. Average velocity = $\frac{10}{4}=2.5$ yards/second. Assuming uniform motion for simplicity (as no other information), velocity in first 2 seconds and last 2 seconds is also 2.5 yards/second.

Step5: Answer for calculating average speed

Average speed = $\frac{\text{total distance traveled}}{\text{total time}}$

Step6: Answer for calculating average velocity

Average velocity = $\frac{\text{total displacement}}{\text{total time}}$

Answer:

5A. 15 yards/second
5B. 15 yards/second
5C. 15 yards/second
6A. 2.5 yards/second
6B. 2.5 yards/second
6C. 2.5 yards/second
7A. Divide the total distance traveled by the total time.
7B. Divide the total displacement by the total time.