Non-Uniform Circular Motion: Locomotive Rounding a Curve

[Becca93]

Homework Statement

As a locomotive rounds a circular curve of radius 2.10 km (which would be 2100 m to keep all the units the same), 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 0.760 m/s2. What is the locomotive's speed at that instant?

After I got it wrong the first few times, I was also given the hint: "The total acceleration is the VECTOR sum of the centripetal acceleration and the tangential acceleration."

Homework Equations

The equations I have in my notes regarding non-uniform circular motion are:
Radial Acceleration: Ar = -(mv^2)/R

Tangential acceleration: At = d|v|/dt

and Total Acceleration: Atot = √(Ar^2 + At^2)

The Attempt at a Solution

To solve, would it be correct to do the following:

Ar = √(Atot^2 - At^2)

And then sub that number into

V = √((RAr)/(-m)

But, if I were to do that, I would get the square root of a negative number, which is an irrational number, which I can't have as a velocity?

Is there a better way to go about this question? What am I doing wrong?

 

[Doc Al]

The equations I have in my notes regarding non-uniform circular motion are:
Radial Acceleration: Ar = -(mv^2)/R

The negative sign just indicates that the acceleration is towards the center. Just worry about the magnitude.

Otherwise your approach is fine.

 

[Becca93]

The negative sign just indicates that the acceleration is towards the center. Just worry about the magnitude.

Otherwise your approach is fine.

But there is no 'm' given in the question, and I don't know how to get radial acceleration any other way.

 

[Doc Al]

But there is no 'm' given in the question, and I don't know how to get radial acceleration any other way.

Oops, I didn't see that. Your equation is not quite right:

The equations I have in my notes regarding non-uniform circular motion are:
Radial Acceleration: Ar = -(mv^2)/R

That's the centripetal force. The radial acceleration is just v^2/R.

 

[Becca93]

Oops, I didn't see that. Your equation is not quite right:

That's the centripetal force. The radial acceleration is just v^2/R.

I must have copied it incorrectly during class. Thank you!