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."
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?