Question

I need help asap please. this is due tonight if you can help. Will mark brainliest

Answer 1

Answer:

The average velocity of the particle during the first two seconds of its movement is $-1.5 \frac{m}{s}$.

Explanation:

When given a graph showing the displacement of an object, the velocity is the slope of the line. This could be problematic if the line is curved and one doesn't know how to calculate derivatives and tangent lines. Thankfully, the lines are linear here.

We can delete the fourth option right away. Because the object has a negative velocity for the two seconds, the average velocity can't be positive like the fourth option.

The velocity of the object at t = 1 second is greater than the velocity of the object at t = 2 seconds. We can use the slope formula $m=\frac{y_2-y_1}{x_2-x_1}$ to find the velocity at each point. To do this, we'll need coordinates, and there are three easy coordinates to use:  $(0,-1)$, $(1, -3)$, and $(2, -4)$.

Now, there are two ways to use those points and the slope formula to solve this. You can calculate the slope for t = 1 second and t = 2 seconds separately, and then find the average, or use the points at t = 0 seconds and t = 2 seconds to find the average slope.

Let's find the separate slopes first. Substituting the points into the slope formula, we get $m=\frac{(-3)-(-1)}{1-0}=\frac{-2}{1} =-2 \frac{m}{s}$ and $m=\frac{(-4)-(-3)}{2-1}=\frac{-1}{1} =-1 \frac{m}{s}$. Since we are looking for the average velocity over 2 seconds, we need to find the average of these values. We get $\frac{(-2)+(-1)}{2} =\frac{(-3)}{2} =-1.5 \frac{m}{s}$.

But what if we calculated the slope between t = 0 seconds and t = 2 seconds, finding the secant line? We'd get $\frac{(-4)-(-1)}{2-0} =\frac{(-3)}{2} =-1.5 \frac{m}{s}$, the exact same answer as above. Hopefully you understand this!