Deceleration problem mechanics

[Breeze]

Hi,
I am reading a book about maths and physics but am stuck on a problem. I don't know where to begin and have tried everything I can think of. The problem is:

'A car is travelling with initial velocity u and applied its brakes. After 2 metres the car's speed is 4 meters per second, and 4 metres after applying the brakes the car stops. What is u and how much time was needed to stop? Assume the car's acceleration (deceleration) is constant, starting from the time the brakes are applied until it stops.'

We are also told, as a hint, to use the fourth equation of motion and the position function.

I have literally run out of ideas. A huge thanks for any solutions or suggestions.

Thanks,
Breeze

 

[Deleted member 4993]

Hi,
I am reading a book about maths and physics but am stuck on a problem. I don't know where to begin and have tried everything I can think of. The problem is:

'A car is travelling with initial velocity u and applied its brakes. After 2 metres the car's speed is 4 meters per second, and 4 metres after applying the brakes the car stops. What is u and how much time was needed to stop? Assume the car's acceleration (deceleration) is constant, starting from the time the brakes are applied until it stops.'

We are also told, as a hint, to use the fourth equation of motion and the position function.

I have literally run out of ideas. A huge thanks for any solutions or suggestions.

Thanks,
Breeze

We are also told, as a hint, to use the fourth equation of motion and the position function.

Can you tell us about the fourth equation of motion - to start with?

Since you have run out of ideas - you must have had several of those ideas. Can you please share with us some of those ideas?

I would suggest - start with a v-t diagram of the car's motion.

 

[topsquark]

Hi,
I am reading a book about maths and physics but am stuck on a problem. I don't know where to begin and have tried everything I can think of. The problem is:

'A car is travelling with initial velocity u and applied its brakes. After 2 metres the car's speed is 4 meters per second, and 4 metres after applying the brakes the car stops. What is u and how much time was needed to stop? Assume the car's acceleration (deceleration) is constant, starting from the time the brakes are applied until it stops.'

We are also told, as a hint, to use the fourth equation of motion and the position function.

I have literally run out of ideas. A huge thanks for any solutions or suggestions.

Thanks,
Breeze

Some general advice:
1) Sketch a diagram
2) Set an origin (where x = 0 m) usually where some kind of motion or change of motion starts.)
3) Label a (set of) positive axis.
4) Make a table of values of what you know... times, positions, velocities, and accelerations.

This will not enable to you to solve all problems. But if you do this then you can show much more easily what you have tried. Even if you don't know what to do you can always use the motion equations to start filling in values of the table you haven't been given.

-Dan

 

[Breeze]

Can you tell us about the fourth equation of motion - to start with?

Since you have run out of ideas - you must have had several of those ideas. Can you please share with us some of those ideas?

I would suggest - start with a v-t diagram of the car's motion.

Hi.
In the book the fourth equation of motion is given as v^2 = u^2 + 2ad. Where v is final velocity and u is initial velocity. I have tried trying to find the acceleration using the so-called fourth equation which for me was 4ms^2. I also tried finding the time, which for me came to 1/2. The book gives the answer as u = 4 x square root of 2 ms. And gives the time to stop as the square root of 2.

 

[Deleted member 4993]

'A car is travelling with initial velocity u and applied its brakes. After 2 metres the car's speed is 4 meters per second,

Write the "fourth equation" for this part treating the initial velocity (u) and deceleration (a) as unknowns.

 

[Breeze]

Write the "fourth equation" for this part treating the initial velocity (u) and deceleration (a) as unknown

I tried that but just get u^2 = 4a. How does the book get 4 x the square root of 2 ?

 

[Deleted member 4993]

Write the "fourth equation" for this part treating the initial velocity (u) and deceleration (a) as unknowns.

What is the final velocity for this part.

Read the question carefully:

A car is travelling with initial velocity u and applied its brakes. After 2 metres the car's speed is 4 meters per second,

And what is the distance travelled (d) for this part?

Rewrite the equation now.

 

[Breeze]

What is the final velocity for this part. 4 ms.

Read the question carefully:



And what is the distance travelled (d) for this part? 2m

Rewrite the equation now. v^2 = 4a + 4^2 I'm still not getting anywhere.

 

[Deleted member 4993]

v^2 = 4a + 4^2 ......................................Incorrect

For the first part of the journey

Initial velocity = u → unknown

Final velocity = v = 4 → m/s

distance travelled = d = 4 meter

acceleration = a → unknown

Equation

v^2 - u^2 = 2*a*d → 16 - u^2 = 2*4*a → u^2 + 8a = 16 .........................................(1)

For the second part of the journey

Initial velocity = 2 m/s

Final velocity = 0 → m/s

distance travelled = 2 meter

acceleration = a → unknown

Equation

0^2 - 4^2 = 2*a*2 → 4 * a = - 16 .................................................................(2)

Two equations and two unknowns (a & u) .............................solve

You are not READING carefully............................