Calculate tangential acceleration knowing velocity and time....

[JulienB]

Homework Statement

A train moves along a circle with radius R = 2 km. The train accelerates with a constant rate, from v₁ = 30 km/h to v₂ = 100 km/h. It crosses S_F = 1200 m during the acceleration.
a) Find the time t_F of the acceleration.
b) What is the tangential acceleration a_T of the train?

Homework Equations

a_T = Δv/Δt
and anything relevant to non-constant displacement along a circle.

The Attempt at a Solution

[/B]
Although it seems pretty easy, I am unsure on how to use the formulas I have. For the first question, I calculated the average speed during the acceleration ((100-30)/2 + 30 = 65 km/h) and then the time it takes at this speed to cross 1.2 km (1 min 6s).

Then I have a lot of different formulas for how to calculate the tangential acceleration, especially that one:
a_T = Δv/Δt

Can someone please help me with how to use this formula in a problem? I would guess Δd is (100 - 30)⋅60² (in order to get a result in m/s) and Δt is 66s, am I right?

Thank you very much in advance for your answers.J.

 

[mfb]

It crosses S_F = 1200 m during the acceleration.

During the acceleration? While it is still accelerating?

Then I have a lot of different formulas for how to calculate the tangential acceleration, especially that one:
a_T = Δv/Δt

Can someone please help me with how to use this formula in a problem? I would guess Δd is (100 - 30)⋅60² (in order to get a result in m/s) and Δt is 66s, am I right?

Why do you need a Δd here (and why should it be different from 1200m?), and where do the factors of 60 come from?

 

[JulienB]

Yes it is still accelerating for 1200m. The factors of 60 are for the velocity to be expressed in m/s, I meant Δv and not Δd of course.

 

[JulienB]

That gives me a tangential acceleration of 3818.2 m/s² btw.

 

[SammyS]

... The factors of 60 are for the velocity to be expressed in m/s, ...

That will give km/s, not m/s.

 

[mfb]

It should give km/(3600h).

That gives me a tangential acceleration of 3818.2 m/s² btw.

That would be lethal.

 

[SammyS]

It should give km/(3600h).

That would be lethal.

Yes, of course!

I stand corrected. DUH!