Question

1. the graph shows the speed of a ball in free fall for 10 seconds. speed of a ball in free fall what is the constant of proportionality shown in the graph?

Explanation:

Step1: Recall the formula for constant of proportionality

The constant of proportionality \( k \) in a proportional relationship \( y = kx \) is given by \( k=\frac{y}{x} \), where \( y \) is the dependent variable (speed here) and \( x \) is the independent variable (time here).

Step2: Pick a point from the graph

From the graph, let's take the point \((10, 100)\) (when \( x = 10 \) seconds, \( y=100 \) meters per second) or we can also take \((1, 10)\), \((2, 20)\) etc. Let's use \((10, 100)\).

Step3: Calculate the constant of proportionality

Using the formula \( k=\frac{y}{x} \), substitute \( x = 10 \) and \( y = 100 \). So \( k=\frac{100}{10}=10 \). We can check with another point, say \((1, 10)\), \( k=\frac{10}{1}=10 \), which is consistent.

Answer:

The constant of proportionality is \( 10 \) (meters per second per second, or \( 10\space m/s^2 \)).