# Homework Help: Calculate tangential acceleration knowing velocity and time...

1. Nov 2, 2015

### JulienB

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

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 SF = 1200 m during the acceleration.
a) Find the time tF of the acceleration.
b) What is the tangential acceleration aT of the train?

2. Relevant equations

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

3. The attempt at a solution

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:
aT = 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?

J.

2. Nov 2, 2015

### Staff: Mentor

During the acceleration? While it is still accelerating?

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

3. Nov 3, 2015

### 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.

4. Nov 3, 2015

### JulienB

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

5. Nov 3, 2015

### SammyS

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

6. Nov 3, 2015

### Staff: Mentor

It should give km/(3600h).

That would be lethal.

7. Nov 3, 2015

### SammyS

Staff Emeritus
Yes, of course!

I stand corrected. DUH!