Tangential and radial train acceleration

[-EquinoX-]

Homework Statement

A train slows down as it rounds a sharp horizontal turn slowing from 90.0 km/h to 50.0km/h in the 15 s that it takes to round the bend. The radius of the curve is 150 m. Compute the acceleration at the moment the train speed reaches 50km/h. Assume it continues to slow down at this time at the same rate.

Homework Equations

The Attempt at a Solution

I think this problem is asking to find the instantaneous velocity at t = 15 sec, which when the speed of the train is 15 sec. From the above information give, we can find the acceleration of the train during from 90-50, which is 11.55 using the formula Vf = volt + 1/2at^2. Then I am stuck here

 

[tiny-tim]

Hi -EquinoX-!

… using the formula Vf = volt + 1/2at^2 …

eugh!

Vf = volt + 1/2at² (and the similar formulas) is only for uniform (constant in magnitude and direction) acceleration.

Hint: the clue's in the title …

tangential and radial acceleration! ​

 

[-EquinoX-]

I know the formula of radial acceleration is ar = V^2/r so is it just 50^2/150?

 

[tiny-tim]

I know the formula of radial acceleration is ar = V^2/r so is it just 50^2/150?

That's right!

(except, of course, you'll have to convert the 50km/h into m/s first )

 

[-EquinoX-]

so it's 192.901/150 = 1.28,

why does the book gives me the information about time?

 

[tiny-tim]

so it's 192.901/150 = 1.28,

why does the book gives me the information about time?

(I make it nearer 1.29)

You'll need the time for the tangential acceleration.

 

[-EquinoX-]

and how is that related? between tangential and acceleration? as far as I know it's dv/dt, but I don't have an equation here to derive...

 

[tiny-tim]

and how is that related? between tangential and acceleration?

Oh come on, -EquinoX-!

You titled this thread "tangential and radial acceleration" …

so you tell us …

what's the formula for tangential acceleration?

 

[-EquinoX-]

ok, my basic instinct says that the 90 can be utilized for something, do we find the acceleration first by (90-50)/15? and yes I know it's in km

 

[tiny-tim]

ok, my basic instinct says that the 90 can be utilized for something, do we find the acceleration first by (90-50)/15? and yes I know it's in km

Yup, that should do it!

i hope you're not going to mention instinct in the exams ​

 

[-EquinoX-]

and does that results in the total acceleration?

and then we can find tangential acceleration from the formula a = sqrt(at^2+ac^2)

 

[tiny-tim]

and does that results in the total acceleration?

and then we can find tangential acceleration from the formula a = sqrt(at^2+ac^2)

No, it's the other way round … the tangential acceleration is (90-50)/15 (I thought that's what you meant in your previous post).

Then the total acceleration (if they want it, which they probably don't) is a = sqrt(at^2+ac^2)

 

[-EquinoX-]

thanks tiny_tim :)