The graph shows the distance of a car from a measuring position located on the edge of a straight road.(a) What was the average velocity of the car from t = 0 to t = 30 seconds?(b) What was the average velocity of the car from t = 10 to t = 30 seconds?(c) About how fast was the car traveling att = 10 seconds? at t = 20 s ? at t = 30 s ? (d) What does the horizontal part of the graph between t = 15 and t = 20 seconds mean?(e) What does the negative velocity at t = 25 represent?

The figure is missing: find it in attachment.

(a)

The average velocity of an object is given by

where:

d is the displacement (the change in position)

t is the time elapsed

Here we want to know the average velocity of the car between t = 0 and t = 30 s, so the time interval is

We notice that:

- at t = 0, the distance from the origin is x = 0

- at t = 30 s, the distance from the origin is x = 300 ft

So, the displacement is:

Therefore, the average velocity in this part is:

(b)

Here we want to find the average velocity from t = 10 to t = 30 seconds.

Given the two points

t = 10 s

t = 30 s

The time elapsed in this case is

On the other hand, we notice that:

- At t = 10 s, the distance from the origin is x = 100 ft

- At t = 30 s, the distance from the origin is x = 300 ft

Therefore, the displacement is

And so, the average velocity of the car in this phase is

(c)

Here we are asked to find how fast is the car going at some precise instants in time: this means, we are asked to find the instantaneous velocity of the car at a certain moments.

This can be found by evaluating the slope of the curve at those precise instants of time.

At t = 10 s, we can estimate the slope by looking at the 5-seconds interval before and after t = 10. We see that in this interval, the distance covered increases by approx 150 ft (from 50 to 200) in a time interval of 10 s, so the instantaneous velocity is approximately

At t = 20 s, the situation is easier: in fact, we see that the curve is horizontal, this means that the slope is zero, so the instantaneous velocity is zero:

Finallly, at t = 30 s, we evaluate the  slope by looking at the few seconds interval before. We see that the distance covered increases by 100 ft in approx. 3 seconds, so the instantaneous velocity at t = 30 s is

(d)

In a distance-time graph, the slope of the graph is equal to the velocity of the graph.

In fact, velocity is the ratio between displacement and time interval

The slope of a graph is given by the ratio between the change in the y-variable and the change in the x-variable:

However for this graph, corresponds to the displacement, while corresponds to the time interval, therefore the slope corresponds to the velocity.

In this graph, the curve between t = 15 s and t = 20 s is horizontal: this means that the slope is zero. Therefore, the velocity of the car in that interval is also zero.

(e)

As we said before, the velocity of the car is the ratio between the displacement and the time interval:

At t = 25 s, the velocity of the car is negative. Looking at the equation, this means that the displacement is also negative. This means that the distance from the origin at a later time is smaller than the distance from the origin at a earlier time.

If we interpret this, it basically means that the car is moving towards the origin, instead that away from it: therefore,

The negative velocity at t = 25 s means that at t = 25 s the car is moving backward, towards the origin.

i leave the calculator work to you.

7. diameter 4 miles, circumference 4π miles

8. radius 0.2 miles, circumference 0.4π miles

[this is a bad problem because the actual radius of a car on the track is less than 0.2 miles so the answer is less than 0.4π miles]

9. radius 6 feet, circumference 12π feet

10. diameter 14 cm, circumference 14π cm

11. diameter 4.8 feet, circumference 4.8π feet

points are handed out whenever you post answers.

brainliest answers are handed out by the person asking the question, so whether your answer is picked depends entirely on whether the asker bothers to pick

if you're asking about your rank, it depends on having a certain number of points and a certain number of brainliest answers. for example, at the time of this writing, i have 44338 points out of 15000 needed for the next (nearly triple the requirement! ) but i only have 24 out of 50 required brainliest answers. this number decays, meaning after a certain amount of time (i think about a month), the total number of brainliest answers you've earned doesn't count toward this total. (i've been stuck at the same rank for a long

the lesson to learn here is that you shouldn't worry about points or rank. chances are, no matter how good an answer you may provide, your efforts will go mostly unnoticed unless you focus on the newest/most active questions that get posted.