Tangential and Radial Acceleration problem

[xChrix]

Homework Statement

As a locomotive rounds a circular curve of radius 1.80 km, its speed is increasing at a rate of 0.440 m/s2. An instrument in the cab (an accelerometer) indicates that the magnitude of the locomotive's total acceleration at a particular instant is 0.680 m/s2. What is the locomotive's speed at that instant?

at = 0.440 m/s^2
a = 0.680 m/s^2
r = 1800 m

Homework Equations

a = sqrt(aradial^2 + atangential^2) (1)

ar = -[(v^2)/r] (2)

The Attempt at a Solution

ar = sqrt(0.440^2 + 0.680^2)

ar= 0.80993

0.80993 = -[v^2 divided by 1800 m]

-38.2 But it is showing up in my online assignment that is it wrong :(

 

[LowlyPion]

Welcome to PF.

I think you almost have it.

It's just that you maybe have switched the sense of what the problem tells you.

You have 2 accelerations as you recognized. Tangential acceleration and Centripetal (Radial).

And the magnitude of their relationship taken together is as I think you figured Radial² + Tangential² = Total²

So far so good. But in the statement of the problem they tell you the Tangential and they tell you the Total, but not the Radial. That's what you need to figure the Tangential velocity.

Just change the way you figured it.

 

[xChrix]

thank you!