Calculating Time and Acceleration in Constantly Accelerating Cars

[Manh]

In a car moving at constant acceleration, you travel 250 m between the instants at which the speedometer reads 40 km/h and 80 km/h.
How many seconds does it take you to travel the 250 m?
What is your acceleration?

I have thought of finding the average of 40 km/h and 80 km/h to start the problem but I'm unsure about that.

 

[Tallus Bryne]

You should use the homework template, to begin with.

There are some basic equations that describe objects under constant acceleration. Have you tried applying them to this situation?

 

[Manh]

I don't receive equations from my teacher but I just looked them up:

http://images.tutorvista.com/cms/images/83/free-fall-formulas.PNG

 

[Manh]

I think the one I found does not apply to this situation. The correct equation may be a = v/t.

 

[LittleMrsMonkey]

You don't know neither the acceleration nor the time interval,so you are going to need one more equation,

 

[Manh]

I have not received any other equation in class and therefore I give it a try by looking up equations around the internet. I just wonder if I'm supposed to find the average speed before I start to do anything else.

 

[Tallus Bryne]

I think the one I found does not apply to this situation. The correct equation may be a = v/t.

Is this a high school class? There should be a textbook or some sort of reference material you have for the course.

The link you posted previously are all special cases of the formulas I was referring to, specifically arranged and simplified for 'free-fall' constant acceleration. The problem is that your object is not under constant 'free-fall' acceleration.

 

[Manh]

I think I might put in it in the wrong section. It is a problem from calculus-based physics on MasteringPhysics and I don't receive any further information beside it.

 

[billy_joule]

This is the correct section. You don't need to resort to using calculus on such a problem.

I have not received any other equation in class and therefore I give it a try by looking up equations around the internet. I just wonder if I'm supposed to find the average speed before I start to do anything else.

No, you don't need to find the average velocity, that won't help.

There is a sticky thread in the forum you posted in with introductory physics formulae:
https://www.physicsforums.com/threads/introductory-physics-formulary.110015/

You have an initial velocity(v₀ ), a final velocity (v) and a displacement (Δx), you want to find the acceleration (a).
Try find the equation that has those.

 

[Tallus Bryne]

I think I might put in it in the wrong section. It is a problem from calculus-based physics on MasteringPhysics and I don't receive any further information beside it.

Do you have access to an e-text through your MasteringPhysics? You need to know the equations of 1-D kinematics to help you solve this problem. I highly doubt that many students will get very far through a calculus based physics course without having some kind of standard reference material to help them, especially if your teacher/professor is not actually providing you with these equations in class in a straightforward way.

 

[Manh]

I found the equations from this link: http://neutrino.otterbein.edu/~tagg/Courses/Current/Phys1500/equation_sheet.pdf
Should I find delta v to apply it to the equation that has t?

 

[billy_joule]

No, you don't need to find the average velocity, that won't help.

Sorry, I was wrong here. Finding V_average will work to find t, the rest of post 9 will help you find a.

I found the equations from this link: http://neutrino.otterbein.edu/~tagg/Courses/Current/Phys1500/equation_sheet.pdf
Should I find delta v to apply it to the equation that has t?

Which one? 4 out of 5 of those equations have t in them...

It's best you make some attempt and we can check it.

 

[Manh]

Should I consider of delta v instead of average v?

 

[Manh]

I see this equation may be helpful: xf = xi + v * delta t.

According to the equation I got approximately 22.50 s after finding delta v and converting all the units.

 

[billy_joule]

That is not correct.

Show you're working (with units) and we'll see where you went wrong.

 

[Manh]

1) delta v = 40 km/h = 11.11 m/s
2) 250 m = 0 m + 11.11 m/s * delta t
3) delta t = 250 m / 11.11 m/s
4) delta t = 22.50 s

 

[LittleMrsMonkey]

1) delta v = 40 km/h = 11.11 m/s
2) 250 m = 0 m + 11.11 m/s * delta t
3) delta t = 250 m / 11.11 m/s
4) delta t = 22.50 s

You take velocity to be constant and equal to 40 km/h.The problem states there is acceleration and the velocity goes up to 80 km/h.
Edit:Sorry,you obviously don't.It's late and my eyes betrayed me.

 

[Manh]

But it also states constant acceleration at the beginning of the problem. I'm very confused!

 

[billy_joule]

But it also states constant acceleration at the beginning of the problem. I'm very confused!

Yes, the car accelerates at a constant rate from 40 to 80 km/hr.

22.5 seconds is the time it take to travel 250 metres traveling at 40 km/hr - Not what you are looking for.

What is the average velocity of the car?
How long does it take to travel 250 metres at that average velocity?

 

[LittleMrsMonkey]

Yes,the problem is you have calculated the average velocity the wrong way.

 

[Manh]

What is the average velocity of the car?
How long does it take to travel 250 metres at that average velocity?

v average = 60 km/h = 16.67 m/s
t = 15 s

Does it look correct now?

 

[LittleMrsMonkey]

Yes,well done.

 

[Manh]

And a = 16.67 m/s / 15 s = 1.11 m/s^2?

 

[billy_joule]

And a = 16.67 m/s / 15 s = 1.11 m/s^2?

No.
It's best to think carefully what it is you have and what it is you want to find before calculating anything.

Acceleration is the rate of change of velocity.
What is the change of velocity in this case?

 

[Manh]

Can I say a = 0 m/s^2 because constant acceleration is mentioned in the problem?

 

[billy_joule]

To change velocity, acceleration must occur. You've already found that change in velocity on page one.

Constant does not mean zero, it means it doesn't change with time. That is, the acceleration is the same for the entire 15 seconds.

 

[Manh]

vf^2 = vi^2 + 2a(delta x)
22.22^2 = 11.11^2 + 2a(250)

Is this the right way to find a?

 

[billy_joule]

The equation you used in post #23 is fine. Though, that equation (in #27) will work it is unnecessarily complicated.

The problem is that you used 16.67 m/s in post #23, that is the average velocity, you need to use the change in velocity.

Acceleration = Change in velocity / change in time

 

[Manh]

a = 11.11 m/s / 15 s
a = 0.74 m/s^2 ?

 

[LittleMrsMonkey]

This would be it.Also,nice work on not forgetting to put the units of measurement after your results.

 

[Manh]

Thank you everyone (billy_joule, LittleMrsMonkey, and Tallus Bryne) for helping me solve the problem. I really appreciate your time to work with me!