# Calculating Time and Acceleration in Constantly Accelerating Cars

• Manh
In summary, 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. The equation that is needed to solve for t is xf = xi + v * delta t.
Manh
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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?

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.

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?

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

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

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.

Manh said:
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.

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.

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

Manh said:
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:

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.

Manh said:
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.

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?

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

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

Manh said:
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.

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Should I consider of delta v instead of average v?

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.

That is not correct.

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

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

Manh said:
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.

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

Manh said:
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?

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

billy_joule said:
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?

Yes,well done.

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

Manh said:
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?

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

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.

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

Is this the right way to find a?

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

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

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

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

## 1. How do you calculate the time it takes for a car to reach a certain speed?

To calculate the time it takes for a car to reach a certain speed, you can use the formula t = (v - u)/a, where t is the time, v is the final velocity, u is the initial velocity, and a is the acceleration. Simply plug in the values and solve for t to get the time in seconds.

## 2. What is the difference between average acceleration and instantaneous acceleration?

Average acceleration is the change in velocity over a period of time, while instantaneous acceleration is the acceleration at a specific moment in time. Average acceleration can be calculated by dividing the change in velocity by the change in time, while instantaneous acceleration can be found by taking the derivative of the velocity function with respect to time.

## 3. How does acceleration affect the time it takes for a car to reach a certain speed?

The greater the acceleration, the shorter the time it takes for a car to reach a certain speed. This is because acceleration is directly proportional to the change in velocity, and the greater the acceleration, the faster the car can reach the desired speed.

## 4. Can you calculate the acceleration of a car if you know the time and distance it traveled?

Yes, you can use the formula a = 2d/t^2, where a is the acceleration, d is the distance, and t is the time. This formula applies to objects that are constantly accelerating, such as a car. However, if the car is not constantly accelerating, you will need more information to calculate its acceleration.

## 5. How can you tell if a car is constantly accelerating?

If a car's velocity is changing at a constant rate, then it is considered to be constantly accelerating. This means that its acceleration is constant and can be calculated using the formula a = (v - u)/t, where v is the final velocity, u is the initial velocity, and t is the time. If the acceleration is not constant, then the car is not constantly accelerating.

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