Question

Please help! Sam is observing the velocity of a car at different times. After two hours the velocity of a car is 54 km/h. After 4 hours the velocity of the car is 58 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the car at different times. Show your work and define the variables used.

Part B: How can you graph the equation obtained in part A for the first 6 hours?

Answer 1

For part A I'm confused but I think standard form is ax + by = c?
And part B would it go (6, _ )

Answer 2

For part B I think the x variable is 6 because that would be the amount of hours and I left the y variable blank because I haven't figured out part A?

Answer 3

Let x = time of observation
and y = observed velocity.

Answer 4

Ok so would it be (6, 60)?

Answer 5

Nope, how did you get the y-coordinate of 60 km/h?

Answer 6

Oh wait would it be 62? I only counted two more instead of four oops

Answer 7

@jchick how did you get that

Answer 8

Yes, 62 km/h is correct :-)

Answer 9

( x hours, y km/h )

Answer 10

Ok so that's one pair of coordinates now do I need another?

Answer 11

It's ok jchick lol

Answer 12

Use the given data.

Answer 13

whilst the answer MAY be correct this is a very ill formed question.

We all know that cars speed varies constantly , and in this particular case there is ABSOLUTELY no reason to assume that the increase in speed is linear over TWO HOURs.

All the data really tells you is the speed at 2 discrete point in time - it NOT valid to interpolate from this data in this case anything about speed at any other time

Answer 14

Mr. Nood that's how the question is said. That's the exact words. Idk what to tell ya.

Answer 15

Given data is given data, just use it please :-)

Answer 16

As I said - it probably expects you to do a straight line interpolation (and that is why I say the answer is correct)

My point is - you should look at your data and what the 'graph' is intended to madel. In this case it is not reasonable to use the 2 points to interpolate any other points.

Answer 17

You need to write an equation, so may as well start with that particular framework.

For now, assume that the car's acc'n is constant, while realizing (a la Mr. Nood) that we don't know that as a fact.

1. Given a constant acc'n, and using the variables t (for time), v (for velocity), and v0 (for initial velocity) can you write a general equation for the velocity of the car?

Answer 18

So how would I word Part B then.
My best answer is "I would plug in 6 for time and 62 for velocity."

Part A I'm still confused on :/

Answer 19

Find the slope.

Answer 20

Part A says standard form. Is the layout for standard form ax + by = c?

Answer 21

Coming up with a general equation for velocity when acc'n is given as a constant, t is time and v0 is the initial velocity, could help you considerably. You need that frameworkf irst. Then, you can concentrate on finding the unknown quantitiies in this general equation using the time and velocity info given.

Answer 22

v = 54 + 2t

v is velocity....t is time in hours

Answer 23

ax+by=c is the equation in standard form of a straight line.

Your question seems to be from Physics: you want an equation for velocity as a function of time, t. Hint: What are other forms of the equation of a straight line? Which applies here?

Answer 24

This question is from algebra 1 haha it does sound like physics though

Answer 25

v0 = initial velocity
v = final velocity
a = acceleration
t = time

Answer 26

v = v0 + at

Answer 27

Even in algebra there are usually brief descriptions and examples of equations of motion, such as the one you need here is.

Answer 28

We know initial velocity v0 = ?

Answer 29

Look at what jchick has submitted: \[v=v _{0}+at\]

Answer 30

Recall $$\huge y= mx+b$$

Answer 31

this is exactly the form I'd been hoping would surface here.

Note that a represents acceleration (which FOR NOW, Mr. Nood, we assume is constant); v is the velocity as a function of time, t, and \[v _{0}\]

Answer 32

is the (for now unknown) initial velocity.

Answer 33

So the initial velocity was 54 right because it's the first velocity they give us right?

Answer 34

Given v0, a and t calculate v
Given initial velocity, acceleration and time calculate the velocity.
v = v0 + at
Given v, a and t calculate v0
Given velocity, acceleration and time calculate the initial velocity.
v0 = v - at
Given v, v0 and t calculate a
Given velocity, initial velocity and time calculate the acceleration.
a = (v - v0)/t
Given v, v0 and a calculate t
Given velocity, initial velocity and acceleration calculate the time.
t = (v - v0)/a

Answer 35

You are given the time and the velocity for two different occasions. Consider these points to be "solutions" of the equation provided by jchick.

Use the usual method(s) to find the equation of the straight line represented by her equation. Find the values of a amd \[v _{0}\] in that manner.

Answer 36

Lot of cooks stirring the soup right now. Kitchen's a bit crowded. I'm stepping out, since there are a lot if capable cooks here. ;)

Answer 37

@mathmale I was thinking the same thing lol

Answer 38

Let's please NOT all abandon ship at once.

Answer 39

Bad, bad spamming. Let's get back to solving the question at hand.

Answer 40

Did you understand what @mathmale was saying on how to solve.

Answer 41

You guys are really smart and obviously know what you're doing but is there any way you can dumb it down? I'm kinda getting lost. :/

Answer 42

I'm voluntarily out again due to the preponderance of expert talent on board.

Answer 43

Ok so in other words as @mathmale said find the equation of the straight line represented by her equation. Find the values of a

Answer 44

@violent_hippie plot the given data:

x hours, y km/h

$$\Huge( 2, 54 ) and ( 4, 58 )$$

Answer 45

That will indeed work. Once you graph that post it.

Answer 46

Forget about (6, 62) for now :-)