Question

the graph shows the momentum of an object as a function of its speed. determine the slope of the line and indicate the units on the slope. momentum (kg·m/s) speed (m/s) slope: units:

Explanation:

Step1: Select two points

Let's take two points from the line: (5, 25) and (10, 50).

Step2: Use slope - formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $y$ represents momentum and $x$ represents speed. So $m=\frac{50 - 25}{10 - 5}$.

Step3: Calculate the slope

$\frac{50 - 25}{10 - 5}=\frac{25}{5}=5$.

Step4: Determine the units

The units of the numerator (momentum) are $\text{kg}\cdot\text{m/s}$ and the units of the denominator (speed) are $\text{m/s}$. So the units of the slope are $\frac{\text{kg}\cdot\text{m/s}}{\text{m/s}}=\text{kg}$.

Answer:

Slope: 5
Units: kg