I get that aN, the normal component is just Kv^2 and got the answer correct. But

Question

I get that aN, the normal component is just Kv^2 and got the answer correct. But i'm confused about how the tangential component ends up at that answer.

A car is entering the circular road whose radius is 30 meters [think the Rotary in Halifax]. Its current speed is 36km/hr but it exits at 42km/hr, after having gone one full circle around the rotary. Estimate the change in the car's speed, and compute its acceleration (i.e. its normal and tangential components) just before the car exits rotary. (answer: aT = 11, 0.0318m/sec2; aN $4.537m/sec2)

Explanation / Answer

radius, r = 30 m
speed, u = 36 km/hr = 10 m/s
final speed, v = 42 km/hr = 11.6667 m/s
this happens after it exits rotary,

so tangential acceleration, at
2*a*(2*pi*r) = v^2 - u^2
2*a*(2*pi*30) = 11.6667^2 - 10^2
a = 0.095789 m/s/s

normal acceleration = v^2/r = 11.6667^2/30 = 4.537 m/s/s

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