# Mechanics Problem, Cannot understand

• mathwurkz
In summary, the car travels rectilinearly with an initial acceleration of 5.0 m/s^2 and reaches a maximum speed of 50 m/s before decelerating at the same rate and coming to a stop in 25 s. The average velocity during this time is 72 km/h. To find the time of uniform motion, we can set up equations for the distance and time traveled during the first and second stages and solve for the system of equations. The result is 15 s.
mathwurkz
Here is the problem.

A car starts moving rectilinearly, first with acceleration $$\omega = 5.0$$ m/s^2 (the initial velocity is equal to zero), then uniformly, and finally, decelerating at the same rate $$\omega$$, comes to a stop. The total time of motion equals $$\tau = 25$$ s. The average velocity during that time is equal to $$v = 72$$ km per hour. How long does the car move uniformly?

If I did not have to deal with the average velocity, then I can figure out that the car will reach a maximum speed of 50 m/s for an instant before it has to decelerate in order to have a 25 s trip. But I think this is where I have a weakness when it comes to average velocities. How do you put it together with acceleration? The answer at the back of my book gives a result of 15 s. I'd appreciate any help getting me pointed in the right direction.

create equations of motion for all three stages of the journey.

For the distance traveled and for the velocities at the end-points of each stage.

Remember that the distance traveled and time taken are the same for the 1st and 3rd stages.

Edit: I got 15s too.

Pretty much what Fermat said:

Find the distance traveled during the first and second states. Note the distance and time displaced during the 3rd stage is the same as the first. So 2*x1+x2 = 500 m and 2t1 + t2 = 25 s. Find the equations for x1 and x2 in terms of t1 and t2, then solve the system of equations.

Thank you I finally solved it. However, what still puzzles me is what the answer at the back gives. I don't understand their interpretation. Then again I don't know if it is even correct since I think there would be a neagtive square root.
What the book gives me:

$$\Delta t = \tau \sqrt{\frac{1-4v}{\omega \tau}} = 15 s$$

## 1. What is mechanics problem?

Mechanics problem refers to a problem or question related to the study of motion and forces, and how they affect the behavior of objects.

## 2. Why is it difficult to understand mechanics problems?

Mechanics problems can be difficult to understand because they often involve complex concepts and mathematical equations that require a strong understanding of physics principles.

## 3. How can I improve my understanding of mechanics problems?

To improve your understanding of mechanics problems, it is important to review and understand the fundamental principles and equations of mechanics, practice solving problems, and seek help from a teacher or tutor if needed.

## 4. What are some common mistakes to avoid when solving mechanics problems?

Some common mistakes to avoid when solving mechanics problems include using incorrect units, not properly setting up the problem or using incorrect equations, and making calculation errors.

## 5. Are there any resources available to help with understanding mechanics problems?

Yes, there are many resources available to help with understanding mechanics problems, such as textbooks, online tutorials and videos, and study guides. It can also be helpful to join a study group or seek help from a teacher or tutor.

• Introductory Physics Homework Help
Replies
8
Views
1K
• Introductory Physics Homework Help
Replies
6
Views
690
• Introductory Physics Homework Help
Replies
20
Views
856
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
11
Views
657
• Introductory Physics Homework Help
Replies
1
Views
538
• Introductory Physics Homework Help
Replies
3
Views
613
• Introductory Physics Homework Help
Replies
19
Views
777
• Introductory Physics Homework Help
Replies
6
Views
209
• Introductory Physics Homework Help
Replies
4
Views
2K