A train slows down at a constant rate as it rounds a sharp circular horizontal turn. Its initial speed is not known. It takes 16.3s to slow down from 74km/h to 40km/h.  The radius of the curve...

A train slows down at a constant rate as it rounds a sharp circular horizontal turn. Its initial speed is not known. It takes 16.3s to slow down from 74km/h to 40km/h.  The radius of the curve is 158m.  As the train goes around the turn, what is the sign of the tangential component of the acceleration?

justaguide | Certified Educator

The train slows down at a constant rate as it rounds a sharp circular horizontal turn. Its initial speed is not known. It takes 16.3 s to slow down from 74 km/h to 40 km/h.  The radius of the curve is 158 m.  As the train goes around the turn, the sign of the tangential component of the acceleration has to be determined.

The initial velocity of the train is 74 km/h = 20.56 m/s. The final velocity of the train is 11.11 m/s. It is seen that the final velocity is lower than the initial velocity. The tangential acceleration of the train is negative. The acceleration is equal to (11.11 - 20.56)/16.3 = -0.579 m/s^2. The negative sign indicates that the tangential acceleration is negative and decelerates the train due to which the final velocity is less than the initial velocity.