1. The problem statement, all variables and given/known data 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." 2. Relevant 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) 3. 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?