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: (10, 25) and (30, 75) where the first - coordinate is speed (in m/s) and the second - coordinate is momentum (in kg·m/s).

Step2: Use slope formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 10$, $y_1 = 25$, $x_2 = 30$, $y_2 = 75$. So $m=\frac{75 - 25}{30 - 10}=\frac{50}{20}=2.5$.

Step3: Determine units

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

Answer:

Slope: 2.5
Units: kg