# Tangential and radial acceleration

1. Sep 29, 2008

### -EquinoX-

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. 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 = Vot + 1/2at^2. Then I am stuck here

2. Sep 29, 2008

### tiny-tim

Hi -EquinoX-!
eugh! :yuck:

Vf = Vot + 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!

3. Sep 29, 2008

### -EquinoX-

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

4. Sep 29, 2008

### tiny-tim

That's right!

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

5. Sep 29, 2008

### -EquinoX-

so it's 192.901/150 = 1.28,

why does the book gives me the information about time?

6. Sep 29, 2008

### tiny-tim

(I make it nearer 1.29)

You'll need the time for the tangential acceleration.

7. Sep 29, 2008

### -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...

Last edited: Sep 29, 2008
8. Sep 29, 2008

### tiny-tim

Oh come on, -EquinoX-!

You titled this thread "tangential and radial acceleration" …

so you tell us

what's the formula for tangential acceleration?

9. Sep 29, 2008

### -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

10. Sep 29, 2008

### tiny-tim

Yup, that should do it!

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

11. Sep 29, 2008

### -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)

12. Sep 29, 2008

### tiny-tim

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)

13. Sep 29, 2008

### -EquinoX-

thanks tiny_tim :)