Math / Data & Statistics

QuestionWeek \#3: Warmup, Th. \& Fri., Sep. 5\&6 Calculate the object's speed shown in the graph.

Studdy Solution

STEP 1

1. The graph shows the position of an object as a function of time.
2. The graph is a straight line, indicating a constant speed.
3. Speed is defined as the change in position divided by the change in time.

STEP 2

1. Determine the coordinates of two points on the line from the graph.
2. Calculate the change in position ( $\Delta y$ ) and the change in time ( $\Delta x$ ).
3. Use the formula for speed: $\text{speed} = \frac{\Delta y}{\Delta x}$ .
4. Provide the final speed value.

STEP 3

Identify the coordinates of two points on the line. From the graph, we can see that the line passes through the points $(0, 0)$ and $(6, 15)$ .

STEP 4

Calculate the change in position ( $\Delta y$ ) using the y-coordinates of the two points.
$\Delta y = y_2 - y_1 = 15 - 0 = 15 \, \text{meters}$

STEP 5

Calculate the change in time ( $\Delta x$ ) using the x-coordinates of the two points.
$\Delta x = x_2 - x_1 = 6 - 0 = 6 \, \text{seconds}$

STEP 6

Use the formula for speed: $\text{speed} = \frac{\Delta y}{\Delta x}$ .
$\text{speed} = \frac{15 \, \text{meters}}{6 \, \text{seconds}} = 2.5 \, \text{meters per second}$

STEP 7

The object's speed is $2.5 \, \text{meters per second}$ .

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