Question

the motion of a lacrosse player is captured using a motion detector and displayed on the graph shown. use the graph to answer the following questions.
right is defined as positive.
answers have a 5% tolerance to allow for estimation.

what is the distance and direction traveled during the following time periods?
0s - 8s: yellow box m , right dropdown
8s - 24s: yellow box m , right dropdown
how far away and in what direction from their starting position does she end up?
yellow box m , right dropdown
describe the lacrosse player’s speed during the following time periods?
0s - 8s: increasing speed dropdown
8s - 24s: decreasing speed dropdown

Explanation:

0s - 8s Distance Calculation

Step1: Identify the graph shape (triangle)

The velocity - time graph from 0s to 8s is a triangle with base \(b = 8\ s\) and height \(h=4\ m/s\). The distance traveled is the area under the velocity - time graph. The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\).

Step2: Calculate the area

Substitute \(base = 8\ s\) and \(height = 4\ m/s\) into the formula: \(A=\frac{1}{2}\times8\times4\)
\(A = 16\ m\)

8s - 24s Distance Calculation

Step1: Identify the graph shape (triangle)

The velocity - time graph from 8s to 24s is a triangle with base \(b=24 - 8=16\ s\) and height \(h = 4\ m/s\). The distance traveled is the area under the velocity - time graph. The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\).

Step2: Calculate the area

Substitute \(base = 16\ s\) and \(height = 4\ m/s\) into the formula: \(A=\frac{1}{2}\times16\times4\)
\(A=32\ m\)

Final Position (Total Distance)

Step1: Sum the two distances

The total distance (displacement, since velocity is always positive) is the sum of the distance from 0 - 8s and 8 - 24s.

Step2: Calculate the sum

\(Total\ distance=16 + 32=48\ m\)

0s - 8s Distance Answer: \(16\)

8s - 24s Distance Answer: \(32\)

Final Position Distance Answer: \(48\)

(For the direction, since velocity is positive (right is positive) throughout, the direction for all these intervals is right.)

Answer:

Step1: Sum the two distances

The total distance (displacement, since velocity is always positive) is the sum of the distance from 0 - 8s and 8 - 24s.

Step2: Calculate the sum

\(Total\ distance=16 + 32=48\ m\)

0s - 8s Distance Answer: \(16\)

8s - 24s Distance Answer: \(32\)

Final Position Distance Answer: \(48\)

(For the direction, since velocity is positive (right is positive) throughout, the direction for all these intervals is right.)