The firetruck goes around a 180°, 162 m radius circular curve. It enters the curve with a speed of 12.6 m/s and leaves the curve with a speed of 38.8 m/s. Assuming the speed changes at a constant rate, what is the magnitude of the total acceleration of the firetruck just after it has entered the curve?

Answer 1

From the length of the curve (L=πr), calculate the average tangential acceleration, At
= (38.8-12.6)/L
Find the radial acceleration due to curvature at entry to curve (v=12.6m/s)
Ar=v²/r
=12.6²/r

Since the two accelerations are perpendicular to each other, add Ar and At vectorially.

Answer 2

I don't understand how you get At = (38.8 - 12.6)/L.Please explain
Thanks.